Best Known (54−35, 54, s)-Nets in Base 25
(54−35, 54, 148)-Net over F25 — Constructive and digital
Digital (19, 54, 148)-net over F25, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 148, using
(54−35, 54, 162)-Net over F25 — Digital
Digital (19, 54, 162)-net over F25, using
- net from sequence [i] based on digital (19, 161)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 162, using
(54−35, 54, 6814)-Net in Base 25 — Upper bound on s
There is no (19, 54, 6815)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 53, 6815)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 123 272867 577174 601004 686256 210077 862412 130804 387368 202185 401814 356639 468905 > 2553 [i]