Best Known (6−4, 6, s)-Nets in Base 7
(6−4, 6, 21)-Net over F7 — Constructive and digital
Digital (2, 6, 21)-net over F7, using
- net defined by OOA [i] based on linear OOA(76, 21, F7, 4, 4) (dual of [(21, 4), 78, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(76, 21, F7, 3, 4) (dual of [(21, 3), 57, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- 1 times truncation [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- appending kth column [i] based on linear OOA(76, 21, F7, 3, 4) (dual of [(21, 3), 57, 5]-NRT-code), using
(6−4, 6, 30)-Net over F7 — Digital
Digital (2, 6, 30)-net over F7, using
- net defined by OOA [i] based on linear OOA(76, 30, F7, 4, 4) (dual of [(30, 4), 114, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(76, 30, F7, 3, 4) (dual of [(30, 3), 84, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(76, 30, F7, 4) (dual of [30, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- 1 times truncation [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(76, 30, F7, 4) (dual of [30, 24, 5]-code), using
- appending kth column [i] based on linear OOA(76, 30, F7, 3, 4) (dual of [(30, 3), 84, 5]-NRT-code), using
(6−4, 6, 79)-Net in Base 7 — Upper bound on s
There is no (2, 6, 80)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(76, 80, S7, 4), but
- the linear programming bound shows that M ≥ 31 342311 / 263 > 76 [i]