Best Known (124−30, 124, s)-Nets in Base 5
(124−30, 124, 408)-Net over F5 — Constructive and digital
Digital (94, 124, 408)-net over F5, using
- 4 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
(124−30, 124, 3161)-Net over F5 — Digital
Digital (94, 124, 3161)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5124, 3161, F5, 30) (dual of [3161, 3037, 31]-code), using
- 32 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 8 times 0, 1, 19 times 0) [i] based on linear OA(5120, 3125, F5, 30) (dual of [3125, 3005, 31]-code), using
- 1 times truncation [i] based on linear OA(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using
- 32 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 8 times 0, 1, 19 times 0) [i] based on linear OA(5120, 3125, F5, 30) (dual of [3125, 3005, 31]-code), using
(124−30, 124, 963504)-Net in Base 5 — Upper bound on s
There is no (94, 124, 963505)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 470 199898 910496 742827 281131 797901 858980 476219 455567 114699 947543 815092 328242 557332 539725 > 5124 [i]