Best Known (19, 19+57, s)-Nets in Base 25
(19, 19+57, 148)-Net over F25 — Constructive and digital
Digital (19, 76, 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+57, 162)-Net over F25 — Digital
Digital (19, 76, 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+57, 2599)-Net in Base 25 — Upper bound on s
There is no (19, 76, 2600)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 75, 2600)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 706 877378 171737 299605 620493 217776 618078 646443 287657 814295 563147 588365 295056 638602 101517 069314 992809 085697 > 2575 [i]