Best Known (23−11, 23, s)-Nets in Base 2
(23−11, 23, 23)-Net over F2 — Constructive and digital
(23−11, 23, 41)-Net over F2 — Upper bound on s (digital)
There is no digital (12, 23, 42)-net over F2, because
- 1 times m-reduction [i] would yield digital (12, 22, 42)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(222, 42, F2, 10) (dual of [42, 20, 11]-code), but
- adding a parity check bit [i] would yield linear OA(223, 43, F2, 11) (dual of [43, 20, 12]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(222, 42, F2, 10) (dual of [42, 20, 11]-code), but
(23−11, 23, 48)-Net in Base 2 — Upper bound on s
There is no (12, 23, 49)-net in base 2, because
- 1 times m-reduction [i] would yield (12, 22, 49)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 4 444056 > 222 [i]