Best Known (96, 96+32, s)-Nets in Base 5
(96, 96+32, 408)-Net over F5 — Constructive and digital
Digital (96, 128, 408)-net over F5, using
- 4 times m-reduction [i] based on digital (96, 132, 408)-net over F5, using
- trace code for nets [i] based on digital (30, 66, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- trace code for nets [i] based on digital (30, 66, 204)-net over F25, using
(96, 96+32, 2719)-Net over F5 — Digital
Digital (96, 128, 2719)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5128, 2719, F5, 32) (dual of [2719, 2591, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(5128, 3133, F5, 32) (dual of [3133, 3005, 33]-code), using
- construction XX applied to Ce(31) ⊂ Ce(30) ⊂ Ce(28) [i] based on
- linear OA(5126, 3125, F5, 32) (dual of [3125, 2999, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(5121, 3125, F5, 31) (dual of [3125, 3004, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(5116, 3125, F5, 29) (dual of [3125, 3009, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(50, 6, F5, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, 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(31) ⊂ Ce(30) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(5128, 3133, F5, 32) (dual of [3133, 3005, 33]-code), using
(96, 96+32, 664096)-Net in Base 5 — Upper bound on s
There is no (96, 128, 664097)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 293876 520023 969330 267926 819945 462539 861200 015380 671351 708623 454341 033883 548360 745577 562049 > 5128 [i]