Best Known (72−56, 72, s)-Nets in Base 25
(72−56, 72, 126)-Net over F25 — Constructive and digital
Digital (16, 72, 126)-net over F25, using
- t-expansion [i] based on digital (10, 72, 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
(72−56, 72, 150)-Net over F25 — Digital
Digital (16, 72, 150)-net over F25, using
- net from sequence [i] based on digital (16, 149)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 16 and N(F) ≥ 150, using
(72−56, 72, 1836)-Net in Base 25 — Upper bound on s
There is no (16, 72, 1837)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 45015 178684 965623 246187 851899 796070 488657 564048 277184 000029 063854 697115 037525 302049 816501 753532 848545 > 2572 [i]