Best Known (19, 19+77, s)-Nets in Base 25
(19, 19+77, 148)-Net over F25 — Constructive and digital
Digital (19, 96, 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
(19, 19+77, 162)-Net over F25 — Digital
Digital (19, 96, 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
(19, 19+77, 1936)-Net in Base 25 — Upper bound on s
There is no (19, 96, 1937)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 95, 1937)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 6 460574 479227 623863 076811 717849 938313 224840 014442 352458 458121 406340 044816 502353 760344 534984 072613 527867 992894 171316 177561 457529 119825 > 2595 [i]