Best Known (67, 67+42, s)-Nets in Base 5
(67, 67+42, 252)-Net over F5 — Constructive and digital
Digital (67, 109, 252)-net over F5, using
- 5 times m-reduction [i] based on digital (67, 114, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 57, 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, 57, 126)-net over F25, using
(67, 67+42, 282)-Net over F5 — Digital
Digital (67, 109, 282)-net over F5, using
(67, 67+42, 9198)-Net in Base 5 — Upper bound on s
There is no (67, 109, 9199)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 15437 135356 366903 802172 871971 541637 507747 862934 764525 688319 417334 904764 836717 > 5109 [i]