Best Known (71, 71+42, s)-Nets in Base 5
(71, 71+42, 252)-Net over F5 — Constructive and digital
Digital (71, 113, 252)-net over F5, using
- 9 times m-reduction [i] based on digital (71, 122, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 61, 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, 61, 126)-net over F25, using
(71, 71+42, 334)-Net over F5 — Digital
Digital (71, 113, 334)-net over F5, using
(71, 71+42, 12503)-Net in Base 5 — Upper bound on s
There is no (71, 113, 12504)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 9 639523 728748 597861 606455 989451 282540 823673 913231 693412 350560 557884 132090 070625 > 5113 [i]