Best Known (109−40, 109, s)-Nets in Base 5
(109−40, 109, 252)-Net over F5 — Constructive and digital
Digital (69, 109, 252)-net over F5, using
- 9 times m-reduction [i] based on digital (69, 118, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 59, 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, 59, 126)-net over F25, using
(109−40, 109, 342)-Net over F5 — Digital
Digital (69, 109, 342)-net over F5, using
(109−40, 109, 13370)-Net in Base 5 — Upper bound on s
There is no (69, 109, 13371)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 15408 611141 139687 536196 521461 178131 319644 095452 043602 280686 884578 424061 156401 > 5109 [i]