Best Known (7, 7+7, s)-Nets in Base 2
(7, 7+7, 20)-Net over F2 — Constructive and digital
Digital (7, 14, 20)-net over F2, using
(7, 7+7, 27)-Net over F2 — Upper bound on s (digital)
There is no digital (7, 14, 28)-net over F2, because
- 1 times m-reduction [i] would yield digital (7, 13, 28)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(213, 28, F2, 6) (dual of [28, 15, 7]-code), but
- adding a parity check bit [i] would yield linear OA(214, 29, F2, 7) (dual of [29, 15, 8]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(213, 28, F2, 6) (dual of [28, 15, 7]-code), but
(7, 7+7, 30)-Net in Base 2 — Upper bound on s
There is no (7, 14, 31)-net in base 2, because
- extracting embedded OOA [i] would yield OOA(214, 31, S2, 2, 7), but
- the linear programming bound for OOAs shows that M ≥ 1 567371 026125 770975 175547 701248 / 88 294887 481723 325628 893545 > 214 [i]