Best Known (126−30, 126, s)-Nets in Base 5
(126−30, 126, 416)-Net over F5 — Constructive and digital
Digital (96, 126, 416)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (33, 48, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 24, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- trace code for nets [i] based on digital (9, 24, 104)-net over F25, using
- digital (48, 78, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 39, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25 (see above)
- trace code for nets [i] based on digital (9, 39, 104)-net over F25, using
- digital (33, 48, 208)-net over F5, using
(126−30, 126, 3285)-Net over F5 — Digital
Digital (96, 126, 3285)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5126, 3285, F5, 30) (dual of [3285, 3159, 31]-code), using
- 154 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 8 times 0, 1, 19 times 0, 1, 42 times 0, 1, 78 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
- 154 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 8 times 0, 1, 19 times 0, 1, 42 times 0, 1, 78 times 0) [i] based on linear OA(5120, 3125, F5, 30) (dual of [3125, 3005, 31]-code), using
(126−30, 126, 1194127)-Net in Base 5 — Upper bound on s
There is no (96, 126, 1194128)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 11754 986402 313877 917490 929290 577619 464679 575564 327420 328151 171451 582423 729846 693903 772225 > 5126 [i]