Best Known (17, 68, s)-Nets in Base 25
(17, 68, 126)-Net over F25 — Constructive and digital
Digital (17, 68, 126)-net over F25, using
- t-expansion [i] based on digital (10, 68, 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
(17, 68, 150)-Net over F25 — Digital
Digital (17, 68, 150)-net over F25, using
- t-expansion [i] based on digital (16, 68, 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
- net from sequence [i] based on digital (16, 149)-sequence over F25, using
(17, 68, 2352)-Net in Base 25 — Upper bound on s
There is no (17, 68, 2353)-net in base 25, because
- 1 times m-reduction [i] would yield (17, 67, 2353)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 4625 082484 922106 676537 781070 674429 670547 091730 752844 756095 550929 034005 806707 098591 553047 825881 > 2567 [i]