Best Known (81, 100, s)-Nets in Base 7
(81, 100, 13074)-Net over F7 — Constructive and digital
Digital (81, 100, 13074)-net over F7, using
- net defined by OOA [i] based on linear OOA(7100, 13074, F7, 19, 19) (dual of [(13074, 19), 248306, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(7100, 117667, F7, 19) (dual of [117667, 117567, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(7100, 117670, F7, 19) (dual of [117670, 117570, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(797, 117649, F7, 19) (dual of [117649, 117552, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(779, 117649, F7, 16) (dual of [117649, 117570, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(18) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(7100, 117670, F7, 19) (dual of [117670, 117570, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(7100, 117667, F7, 19) (dual of [117667, 117567, 20]-code), using
(81, 100, 99816)-Net over F7 — Digital
Digital (81, 100, 99816)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(7100, 99816, F7, 19) (dual of [99816, 99716, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(7100, 117670, F7, 19) (dual of [117670, 117570, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(797, 117649, F7, 19) (dual of [117649, 117552, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(779, 117649, F7, 16) (dual of [117649, 117570, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(18) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(7100, 117670, F7, 19) (dual of [117670, 117570, 20]-code), using
(81, 100, large)-Net in Base 7 — Upper bound on s
There is no (81, 100, large)-net in base 7, because
- 17 times m-reduction [i] would yield (81, 83, large)-net in base 7, but