Best Known (14, 14+15, s)-Nets in Base 2
(14, 14+15, 16)-Net over F2 — Constructive and digital
Digital (14, 29, 16)-net over F2, using
(14, 14+15, 37)-Net over F2 — Upper bound on s (digital)
There is no digital (14, 29, 38)-net over F2, because
- 1 times m-reduction [i] would yield digital (14, 28, 38)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(228, 38, F2, 14) (dual of [38, 10, 15]-code), but
- adding a parity check bit [i] would yield linear OA(229, 39, F2, 15) (dual of [39, 10, 16]-code), but
- “Bou†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(229, 39, F2, 15) (dual of [39, 10, 16]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(228, 38, F2, 14) (dual of [38, 10, 15]-code), but
(14, 14+15, 43)-Net in Base 2 — Upper bound on s
There is no (14, 29, 44)-net in base 2, because
- 1 times m-reduction [i] would yield (14, 28, 44)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(228, 44, S2, 14), but
- the linear programming bound shows that M ≥ 449897 824256 / 1547 > 228 [i]
- extracting embedded orthogonal array [i] would yield OA(228, 44, S2, 14), but