Best Known (62, 62+42, s)-Nets in Base 5
(62, 62+42, 252)-Net over F5 — Constructive and digital
Digital (62, 104, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 52, 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
(62, 62+42, 6265)-Net in Base 5 — Upper bound on s
There is no (62, 104, 6266)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 4 941561 246696 866819 271607 774923 664397 974448 032246 702292 163908 729572 315625 > 5104 [i]