Best Known (115−47, 115, s)-Nets in Base 5
(115−47, 115, 252)-Net over F5 — Constructive and digital
Digital (68, 115, 252)-net over F5, using
- 1 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
(115−47, 115, 6851)-Net in Base 5 — Upper bound on s
There is no (68, 115, 6852)-net in base 5, because
- 1 times m-reduction [i] would yield (68, 114, 6852)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 48 200475 823527 223049 746035 113481 627280 572641 541486 185155 415034 081117 899081 582225 > 5114 [i]