Best Known (126−32, 126, s)-Nets in Base 5
(126−32, 126, 408)-Net over F5 — Constructive and digital
Digital (94, 126, 408)-net over F5, using
- 2 times m-reduction [i] based on digital (94, 128, 408)-net over F5, using
- trace code for nets [i] based on digital (30, 64, 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, 64, 204)-net over F25, using
(126−32, 126, 2440)-Net over F5 — Digital
Digital (94, 126, 2440)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5126, 2440, F5, 32) (dual of [2440, 2314, 33]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(5126, 3125, F5, 32) (dual of [3125, 2999, 33]-code), using
(126−32, 126, 543073)-Net in Base 5 — Upper bound on s
There is no (94, 126, 543074)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 11755 242368 286070 771393 578255 006091 776464 535044 561843 640699 720455 888289 355279 937281 446657 > 5126 [i]