Best Known (23−12, 23, s)-Nets in Base 2
(23−12, 23, 15)-Net over F2 — Constructive and digital
Digital (11, 23, 15)-net over F2, using
- 22 times duplication [i] based on digital (9, 21, 15)-net over F2, using
(23−12, 23, 29)-Net over F2 — Upper bound on s (digital)
There is no digital (11, 23, 30)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(223, 30, F2, 12) (dual of [30, 7, 13]-code), but
- adding a parity check bit [i] would yield linear OA(224, 31, F2, 13) (dual of [31, 7, 14]-code), but
- “vT3†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(224, 31, F2, 13) (dual of [31, 7, 14]-code), but
(23−12, 23, 31)-Net in Base 2 — Upper bound on s
There is no (11, 23, 32)-net in base 2, because
- extracting embedded OOA [i] would yield OOA(223, 32, S2, 2, 12), but
- the linear programming bound for OOAs shows that M ≥ 15648 453898 969945 210880 / 1798 548815 076741 > 223 [i]