Best Known (10, 19, s)-Nets in Base 2
(10, 19, 23)-Net over F2 — Constructive and digital
Digital (10, 19, 23)-net over F2, using
(10, 19, 34)-Net over F2 — Upper bound on s (digital)
There is no digital (10, 19, 35)-net over F2, because
- 1 times m-reduction [i] would yield digital (10, 18, 35)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(218, 35, F2, 8) (dual of [35, 17, 9]-code), but
(10, 19, 44)-Net in Base 2 — Upper bound on s
There is no (10, 19, 45)-net in base 2, because
- 1 times m-reduction [i] would yield (10, 18, 45)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 265831 > 218 [i]