Best Known (6, 14, s)-Nets in Base 7
(6, 14, 28)-Net over F7 — Constructive and digital
Digital (6, 14, 28)-net over F7, using
- 1 times m-reduction [i] based on digital (6, 15, 28)-net over F7, using
(6, 14, 32)-Net over F7 — Digital
Digital (6, 14, 32)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(714, 32, F7, 8) (dual of [32, 18, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(714, 52, F7, 8) (dual of [52, 38, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(713, 49, F7, 8) (dual of [49, 36, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(711, 49, F7, 6) (dual of [49, 38, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(71, 3, F7, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(714, 52, F7, 8) (dual of [52, 38, 9]-code), using
(6, 14, 332)-Net in Base 7 — Upper bound on s
There is no (6, 14, 333)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 681411 378529 > 714 [i]