Best Known (99, 99+30, s)-Nets in Base 5
(99, 99+30, 460)-Net over F5 — Constructive and digital
Digital (99, 129, 460)-net over F5, using
- 1 times m-reduction [i] based on digital (99, 130, 460)-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 (51, 82, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 41, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 41, 126)-net over F25, using
- digital (33, 48, 208)-net over F5, using
- (u, u+v)-construction [i] based on
(99, 99+30, 3770)-Net over F5 — Digital
Digital (99, 129, 3770)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5129, 3770, F5, 30) (dual of [3770, 3641, 31]-code), using
- 636 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, 1, 124 times 0, 1, 164 times 0, 1, 191 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
- 636 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, 1, 124 times 0, 1, 164 times 0, 1, 191 times 0) [i] based on linear OA(5120, 3125, F5, 30) (dual of [3125, 3005, 31]-code), using
(99, 99+30, 1647577)-Net in Base 5 — Upper bound on s
There is no (99, 129, 1647578)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 469374 594533 724205 468973 604205 897365 014151 894048 325106 476125 327204 033773 187768 170995 780745 > 5129 [i]