Best Known (96, 96+24, s)-Nets in Base 5
(96, 96+24, 1304)-Net over F5 — Constructive and digital
Digital (96, 120, 1304)-net over F5, using
- net defined by OOA [i] based on linear OOA(5120, 1304, F5, 24, 24) (dual of [(1304, 24), 31176, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(5120, 15648, F5, 24) (dual of [15648, 15528, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5120, 15649, F5, 24) (dual of [15649, 15529, 25]-code), using
- construction XX applied to Ce(23) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(53, 22, F5, 2) (dual of [22, 19, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(23) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(5120, 15649, F5, 24) (dual of [15649, 15529, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(5120, 15648, F5, 24) (dual of [15648, 15528, 25]-code), using
(96, 96+24, 13649)-Net over F5 — Digital
Digital (96, 120, 13649)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5120, 13649, F5, 24) (dual of [13649, 13529, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5120, 15649, F5, 24) (dual of [15649, 15529, 25]-code), using
- construction XX applied to Ce(23) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(53, 22, F5, 2) (dual of [22, 19, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(23) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(5120, 15649, F5, 24) (dual of [15649, 15529, 25]-code), using
(96, 96+24, large)-Net in Base 5 — Upper bound on s
There is no (96, 120, large)-net in base 5, because
- 22 times m-reduction [i] would yield (96, 98, large)-net in base 5, but