Best Known (13, 13+79, s)-Nets in Base 25
(13, 13+79, 126)-Net over F25 — Constructive and digital
Digital (13, 92, 126)-net over F25, using
- t-expansion [i] based on digital (10, 92, 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+79, 1151)-Net in Base 25 — Upper bound on s
There is no (13, 92, 1152)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 91, 1152)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 16 394123 470514 358418 777869 028467 621699 715449 833280 510879 710662 406472 222970 476619 731792 225814 693876 922471 235092 771478 961033 626625 > 2591 [i]