Best Known (19, 19+91, s)-Nets in Base 25
(19, 19+91, 148)-Net over F25 — Constructive and digital
Digital (19, 110, 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+91, 162)-Net over F25 — Digital
Digital (19, 110, 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+91, 1763)-Net in Base 25 — Upper bound on s
There is no (19, 110, 1764)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 109, 1764)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 243 270657 060916 442464 021128 529654 929156 761702 639661 929151 676475 739821 269955 847995 605500 652566 299003 960601 528926 557066 011844 637555 862006 640344 731914 009825 > 25109 [i]