Best Known (107−40, 107, s)-Nets in Base 5
(107−40, 107, 252)-Net over F5 — Constructive and digital
Digital (67, 107, 252)-net over F5, using
- 7 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
(107−40, 107, 313)-Net over F5 — Digital
Digital (67, 107, 313)-net over F5, using
(107−40, 107, 11381)-Net in Base 5 — Upper bound on s
There is no (67, 107, 11382)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 617 305330 265042 638706 244378 473814 474562 949487 005749 147392 284679 691791 893825 > 5107 [i]