Best Known (65, 65+30, s)-Nets in Base 5
(65, 65+30, 258)-Net over F5 — Constructive and digital
Digital (65, 95, 258)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (0, 15, 6)-net over F5, using
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 0 and N(F) ≥ 6, using
- the rational function field F5(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- digital (50, 80, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 40, 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, 40, 126)-net over F25, using
- digital (0, 15, 6)-net over F5, using
(65, 65+30, 609)-Net over F5 — Digital
Digital (65, 95, 609)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(595, 609, F5, 30) (dual of [609, 514, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(595, 624, F5, 30) (dual of [624, 529, 31]-code), using
(65, 65+30, 42895)-Net in Base 5 — Upper bound on s
There is no (65, 95, 42896)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 2 525133 872013 975779 301450 757049 193076 705439 417083 284383 929272 198721 > 595 [i]