Best Known (108−40, 108, s)-Nets in Base 5
(108−40, 108, 252)-Net over F5 — Constructive and digital
Digital (68, 108, 252)-net over F5, using
- 8 times m-reduction [i] based on digital (68, 116, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 58, 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, 58, 126)-net over F25, using
(108−40, 108, 327)-Net over F5 — Digital
Digital (68, 108, 327)-net over F5, using
(108−40, 108, 12335)-Net in Base 5 — Upper bound on s
There is no (68, 108, 12336)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 3081 496541 713745 827808 107060 400841 657406 990432 954677 586312 136612 887233 275905 > 5108 [i]