Best Known (19, 19+69, s)-Nets in Base 25
(19, 19+69, 148)-Net over F25 — Constructive and digital
Digital (19, 88, 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+69, 162)-Net over F25 — Digital
Digital (19, 88, 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+69, 2111)-Net in Base 25 — Upper bound on s
There is no (19, 88, 2112)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 87, 2112)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 41 793711 952952 619316 315321 445197 197762 411723 488813 263447 741664 934850 980530 040242 749264 775526 078575 774856 829943 549005 599745 > 2587 [i]