Best Known (74, 74+42, s)-Nets in Base 5
(74, 74+42, 252)-Net over F5 — Constructive and digital
Digital (74, 116, 252)-net over F5, using
- 12 times m-reduction [i] based on digital (74, 128, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 64, 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, 64, 126)-net over F25, using
(74, 74+42, 379)-Net over F5 — Digital
Digital (74, 116, 379)-net over F5, using
(74, 74+42, 15739)-Net in Base 5 — Upper bound on s
There is no (74, 116, 15740)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1204 603438 307788 540447 780849 735533 283574 646498 604256 852267 436312 727484 858356 900465 > 5116 [i]