Best Known (68−24, 68, s)-Nets in Base 5
(68−24, 68, 252)-Net over F5 — Constructive and digital
Digital (44, 68, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 34, 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
(68−24, 68, 286)-Net over F5 — Digital
Digital (44, 68, 286)-net over F5, using
(68−24, 68, 12073)-Net in Base 5 — Upper bound on s
There is no (44, 68, 12074)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 339049 906462 003966 961028 418455 465637 876695 860673 > 568 [i]