Best Known (13, 13+69, s)-Nets in Base 25
(13, 13+69, 126)-Net over F25 — Constructive and digital
Digital (13, 82, 126)-net over F25, using
- t-expansion [i] based on digital (10, 82, 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+69, 1188)-Net in Base 25 — Upper bound on s
There is no (13, 82, 1189)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 81, 1189)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 171124 779530 959988 466638 737509 141109 117460 388199 171784 634491 526885 732493 267915 432293 544249 330546 155086 499756 867505 > 2581 [i]