Best Known (13, 13+73, s)-Nets in Base 25
(13, 13+73, 126)-Net over F25 — Constructive and digital
Digital (13, 86, 126)-net over F25, using
- t-expansion [i] based on digital (10, 86, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(13, 13+73, 1170)-Net in Base 25 — Upper bound on s
There is no (13, 86, 1171)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 85, 1171)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 68527 601500 136394 042950 267608 096130 050089 234813 529802 030283 776783 271777 762670 096226 889777 374602 219459 682720 326633 553185 > 2585 [i]