Best Known (97, 97+32, s)-Nets in Base 5
(97, 97+32, 408)-Net over F5 — Constructive and digital
Digital (97, 129, 408)-net over F5, using
- 5 times m-reduction [i] based on digital (97, 134, 408)-net over F5, using
- trace code for nets [i] based on digital (30, 67, 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, 67, 204)-net over F25, using
(97, 97+32, 2870)-Net over F5 — Digital
Digital (97, 129, 2870)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5129, 2870, F5, 32) (dual of [2870, 2741, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(5129, 3138, F5, 32) (dual of [3138, 3009, 33]-code), using
- construction X applied to Ce(31) ⊂ 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(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(53, 13, F5, 2) (dual of [13, 10, 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
- construction X applied to Ce(31) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(5129, 3138, F5, 32) (dual of [3138, 3009, 33]-code), using
(97, 97+32, 734374)-Net in Base 5 — Upper bound on s
There is no (97, 129, 734375)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 469383 717677 667950 855001 181802 717359 917726 203073 911195 387816 374047 717319 388641 284189 400001 > 5129 [i]