Best Known (40, 123, s)-Nets in Base 5
(40, 123, 78)-Net over F5 — Constructive and digital
Digital (40, 123, 78)-net over F5, using
- t-expansion [i] based on digital (38, 123, 78)-net over F5, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
(40, 123, 455)-Net in Base 5 — Upper bound on s
There is no (40, 123, 456)-net in base 5, because
- 1 times m-reduction [i] would yield (40, 122, 456)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 19 833076 773038 783897 773798 245605 121102 963287 240099 821282 350260 755852 982483 112099 931425 > 5122 [i]