Best Known (12, 12+12, s)-Nets in Base 2
(12, 12+12, 15)-Net over F2 — Constructive and digital
Digital (12, 24, 15)-net over F2, using
- 23 times duplication [i] based on digital (9, 21, 15)-net over F2, using
(12, 12+12, 32)-Net over F2 — Upper bound on s (digital)
There is no digital (12, 24, 33)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(224, 33, F2, 12) (dual of [33, 9, 13]-code), but
(12, 12+12, 39)-Net in Base 2 — Upper bound on s
There is no (12, 24, 40)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(224, 40, S2, 12), but
- the linear programming bound shows that M ≥ 117037 858816 / 6615 > 224 [i]