Best Known (129−33, 129, s)-Nets in Base 5
(129−33, 129, 408)-Net over F5 — Constructive and digital
Digital (96, 129, 408)-net over F5, using
- 3 times m-reduction [i] based on digital (96, 132, 408)-net over F5, using
- trace code for nets [i] based on digital (30, 66, 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, 66, 204)-net over F25, using
(129−33, 129, 2117)-Net over F5 — Digital
Digital (96, 129, 2117)-net over F5, using
(129−33, 129, 664096)-Net in Base 5 — Upper bound on s
There is no (96, 129, 664097)-net in base 5, because
- 1 times m-reduction [i] would yield (96, 128, 664097)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 293876 520023 969330 267926 819945 462539 861200 015380 671351 708623 454341 033883 548360 745577 562049 > 5128 [i]