Best Known (69−57, 69, s)-Nets in Base 25
(69−57, 69, 126)-Net over F25 — Constructive and digital
Digital (12, 69, 126)-net over F25, using
- t-expansion [i] based on digital (10, 69, 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
(69−57, 69, 1154)-Net in Base 25 — Upper bound on s
There is no (12, 69, 1155)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 68, 1155)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 116702 041580 366371 427190 406906 886119 238202 336174 726573 819494 237386 759420 831101 040218 268772 714209 > 2568 [i]