Best Known (54, 54+51, s)-Nets in Base 5
(54, 54+51, 82)-Net over F5 — Constructive and digital
Digital (54, 105, 82)-net over F5, using
- t-expansion [i] based on digital (48, 105, 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
(54, 54+51, 119)-Net over F5 — Digital
Digital (54, 105, 119)-net over F5, using
(54, 54+51, 2039)-Net in Base 5 — Upper bound on s
There is no (54, 105, 2040)-net in base 5, because
- 1 times m-reduction [i] would yield (54, 104, 2040)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 4 988863 491064 296985 703933 599422 951741 331804 800585 657641 577053 884593 774049 > 5104 [i]