Best Known (125−48, 125, s)-Nets in Base 5
(125−48, 125, 252)-Net over F5 — Constructive and digital
Digital (77, 125, 252)-net over F5, using
- 9 times m-reduction [i] based on digital (77, 134, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 67, 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, 67, 126)-net over F25, using
(125−48, 125, 319)-Net over F5 — Digital
Digital (77, 125, 319)-net over F5, using
(125−48, 125, 10692)-Net in Base 5 — Upper bound on s
There is no (77, 125, 10693)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 2355 906276 449790 795369 871357 172043 253416 975654 031449 764762 507869 257823 418113 933147 672225 > 5125 [i]