Best Known (95−18, 95, s)-Nets in Base 7
(95−18, 95, 13074)-Net over F7 — Constructive and digital
Digital (77, 95, 13074)-net over F7, using
- 71 times duplication [i] based on digital (76, 94, 13074)-net over F7, using
- net defined by OOA [i] based on linear OOA(794, 13074, F7, 18, 18) (dual of [(13074, 18), 235238, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(794, 117666, F7, 18) (dual of [117666, 117572, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(794, 117670, F7, 18) (dual of [117670, 117576, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- linear OA(791, 117649, F7, 18) (dual of [117649, 117558, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(773, 117649, F7, 15) (dual of [117649, 117576, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(73, 21, F7, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(794, 117670, F7, 18) (dual of [117670, 117576, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(794, 117666, F7, 18) (dual of [117666, 117572, 19]-code), using
- net defined by OOA [i] based on linear OOA(794, 13074, F7, 18, 18) (dual of [(13074, 18), 235238, 19]-NRT-code), using
(95−18, 95, 104544)-Net over F7 — Digital
Digital (77, 95, 104544)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(795, 104544, F7, 18) (dual of [104544, 104449, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(795, 117671, F7, 18) (dual of [117671, 117576, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(794, 117670, F7, 18) (dual of [117670, 117576, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- linear OA(791, 117649, F7, 18) (dual of [117649, 117558, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(773, 117649, F7, 15) (dual of [117649, 117576, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(73, 21, F7, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(794, 117670, F7, 18) (dual of [117670, 117576, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(795, 117671, F7, 18) (dual of [117671, 117576, 19]-code), using
(95−18, 95, large)-Net in Base 7 — Upper bound on s
There is no (77, 95, large)-net in base 7, because
- 16 times m-reduction [i] would yield (77, 79, large)-net in base 7, but