Best Known (49, 49+69, s)-Nets in Base 5
(49, 49+69, 82)-Net over F5 — Constructive and digital
Digital (49, 118, 82)-net over F5, using
- t-expansion [i] based on digital (48, 118, 82)-net over F5, using
- net from sequence [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- net from sequence [i] based on digital (48, 81)-sequence over F5, using
(49, 49+69, 96)-Net over F5 — Digital
Digital (49, 118, 96)-net over F5, using
- net from sequence [i] based on digital (49, 95)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 49 and N(F) ≥ 96, using
(49, 49+69, 835)-Net in Base 5 — Upper bound on s
There is no (49, 118, 836)-net in base 5, because
- 1 times m-reduction [i] would yield (49, 117, 836)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 6103 697120 176112 381056 171475 909102 149376 494345 667090 173324 426676 270186 739294 682305 > 5117 [i]