Best Known (13−4, 13, s)-Nets in Base 2
(13−4, 13, 80)-Net over F2 — Constructive and digital
Digital (9, 13, 80)-net over F2, using
(13−4, 13, 81)-Net over F2 — Digital
Digital (9, 13, 81)-net over F2, using
- net defined by OOA [i] based on linear OOA(213, 81, F2, 4, 4) (dual of [(81, 4), 311, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(213, 81, F2, 3, 4) (dual of [(81, 3), 230, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(213, 81, F2, 4) (dual of [81, 68, 5]-code), using
- 1 times truncation [i] based on linear OA(214, 82, F2, 5) (dual of [82, 68, 6]-code), using
- a “Sh1†code from Brouwer’s database [i]
- 1 times truncation [i] based on linear OA(214, 82, F2, 5) (dual of [82, 68, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(213, 81, F2, 4) (dual of [81, 68, 5]-code), using
- appending kth column [i] based on linear OOA(213, 81, F2, 3, 4) (dual of [(81, 3), 230, 5]-NRT-code), using
(13−4, 13, 124)-Net in Base 2 — Upper bound on s
There is no (9, 13, 125)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(213, 125, S2, 4), but
- the linear programming bound shows that M ≥ 15 460480 / 1877 > 213 [i]