Best Known (131−54, 131, s)-Nets in Base 5
(131−54, 131, 252)-Net over F5 — Constructive and digital
Digital (77, 131, 252)-net over F5, using
- 3 times m-reduction [i] based on digital (77, 134, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 67, 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, 67, 126)-net over F25, using
(131−54, 131, 256)-Net over F5 — Digital
Digital (77, 131, 256)-net over F5, using
(131−54, 131, 6704)-Net in Base 5 — Upper bound on s
There is no (77, 131, 6705)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 36 800743 904288 589711 836349 872221 661549 497743 874077 985162 155331 356026 299474 672250 892347 194717 > 5131 [i]