Best Known (109−91, 109, s)-Nets in Base 25
(109−91, 109, 126)-Net over F25 — Constructive and digital
Digital (18, 109, 126)-net over F25, using
- t-expansion [i] based on digital (10, 109, 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
(109−91, 109, 153)-Net over F25 — Digital
Digital (18, 109, 153)-net over F25, using
- net from sequence [i] based on digital (18, 152)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 18 and N(F) ≥ 153, using
(109−91, 109, 1639)-Net in Base 25 — Upper bound on s
There is no (18, 109, 1640)-net in base 25, because
- 1 times m-reduction [i] would yield (18, 108, 1640)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 9 576998 898909 846082 937298 825872 366162 574891 348844 879790 319039 457174 214578 088059 348520 621855 599104 337712 514477 722678 125333 127277 788630 155514 212949 241025 > 25108 [i]