Best Known (80−64, 80, s)-Nets in Base 25
(80−64, 80, 126)-Net over F25 — Constructive and digital
Digital (16, 80, 126)-net over F25, using
- t-expansion [i] based on digital (10, 80, 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
(80−64, 80, 150)-Net over F25 — Digital
Digital (16, 80, 150)-net over F25, using
- net from sequence [i] based on digital (16, 149)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 16 and N(F) ≥ 150, using
(80−64, 80, 1648)-Net in Base 25 — Upper bound on s
There is no (16, 80, 1649)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 6894 089662 033537 985353 166291 086026 317894 475171 287623 378544 548903 088117 336131 876356 505357 521637 013013 410962 984705 > 2580 [i]