Best Known (19, 19+27, s)-Nets in Base 25
(19, 19+27, 148)-Net over F25 — Constructive and digital
Digital (19, 46, 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+27, 162)-Net over F25 — Digital
Digital (19, 46, 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+27, 16294)-Net in Base 25 — Upper bound on s
There is no (19, 46, 16295)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 45, 16295)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 808 050352 505300 635693 340740 909480 328002 248559 431964 861943 373193 > 2545 [i]