6D $(1,0)$ supersymmetry from properties of 6D spinors It is known from string/M-theory considerations that six dimensional superconformal field theories exist with $(1,0)$ supersymmetry. 
But if one looks at Table 2.4 on page 47 of Sergio Cecotti's book, ''Supersymmetric Field Theories: Geometric Structure and Dualities", one finds that $(1,0)$ is not an entry for $d = 6$ in the list of physically allowed supersymmetries. The link to the table is https://books.google.com/books?id=qpiiBQAAQBAJ&lpg=PP1&pg=PA47#v=onepage&q&f=false. One can similarly also look at page 42 of Cecotti's notes (available at http://people.sissa.it/~cecotti/partsI-IIv4.pdf), on which this book is based.
Am I missing some point here? I would expect a $d = 6$ $(1,0)$ SUSY theory to have 4 multiplets with 8 supercharges (a SUGRA multiplet, a tensor multiplet, a vector and a hypermultiplet). Why is this entry missing from the book and notes above?
 A: The problem you are facing is notation. Usually people use the number $\mathcal{N}$ to count the number of supersymmetries such that when $\mathcal{N}=1$ or $(1,0)$ we have the smallest possible supersymmetry. 
In $d=5+1$ a chiral spinor will be of the form $\chi^{I}$, with $I=1,\dots,4$ being a fundamental representation of $SU^{*}(4)$. The supercharges must close under complex conjugation $(\chi^{I})^{*}=\Omega_{IJ}\bar\chi^{J}$, and since the complex conjugation matrix $\Omega_{IJ}$ is anti-symmetric and squares to $-1$ it is impossible to use a single chiral spinor $Q^{I}$ and impose a Majorana constraint $\bar Q^{I}=Q^{I}$, without forcing $Q^{I}=0$. 
However, if we have two chiral spinors $Q^{I}_{a}$, with $a=1,2$, it is possible to construct the following constraint:
$$
(Q^{I}_{a})^{*}=\varepsilon^{ab}\Omega_{IJ}Q^{J}_{b}
$$
Note that this constraint relates the spinor $Q_{1}^{I}$ with the complex conjugation of the spinor $Q_{2}^{I}$, and vice-versa. If we define $\bar \chi^{I}_{a}=\varepsilon_{ab}\Omega^{IJ}(\chi^{J}_{b})^{*}$ the constraint above becomes
$$
\bar Q_{a}^{I}=Q_{a}^{I}
$$
This $SU(2)$ symmetry becomes the $R$-symmetry if we dimensionaly reduce this $d=1+5$ theory into a $d=1+3$ theory. We can also break this $SU(2)$ symmetry by picking $Q_{1}\equiv Q$ and $Q_{2}\equiv\bar Q$ and constructing a single unconstrained chiral spinor $Q^{I}$, with 4 complex components and 8 real components. If we parametrize the breaking of this $SU(2)$ by an harmonic variable $SU(2)/U(1)$, before dimensional reduction to $d=1+3$ we obtain the harmonic superspace formalism. 
Usually people call this pair of two chiral spinor obeying the constraint above, or the equivalent single chiral unconstrained spinor, by $\mathcal{N}=(1,0)$, a theory with 8 supercharges in total.
