Best Known (19, 19+79, s)-Nets in Base 25
(19, 19+79, 148)-Net over F25 — Constructive and digital
Digital (19, 98, 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+79, 162)-Net over F25 — Digital
Digital (19, 98, 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+79, 1903)-Net in Base 25 — Upper bound on s
There is no (19, 98, 1904)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 97, 1904)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 4052 438938 496455 722471 803944 147465 897542 356944 307752 183151 309107 484860 035324 544724 397305 915484 110486 239459 380813 248271 360671 207648 970625 > 2597 [i]