Best Known (85, 85+58, s)-Nets in Base 5
(85, 85+58, 252)-Net over F5 — Constructive and digital
Digital (85, 143, 252)-net over F5, using
- 7 times m-reduction [i] based on digital (85, 150, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 75, 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, 75, 126)-net over F25, using
(85, 85+58, 292)-Net over F5 — Digital
Digital (85, 143, 292)-net over F5, using
(85, 85+58, 8139)-Net in Base 5 — Upper bound on s
There is no (85, 143, 8140)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 8997 339860 283641 245495 309433 744572 866393 020752 300643 652460 945731 559658 205026 721500 949393 846467 509425 > 5143 [i]