Best Known (109−94, 109, s)-Nets in Base 25
(109−94, 109, 126)-Net over F25 — Constructive and digital
Digital (15, 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
(109−94, 109, 140)-Net over F25 — Digital
Digital (15, 109, 140)-net over F25, using
- net from sequence [i] based on digital (15, 139)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 15 and N(F) ≥ 140, using
(109−94, 109, 1311)-Net in Base 25 — Upper bound on s
There is no (15, 109, 1312)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 241 668843 157763 426606 658434 053116 931013 870024 291036 134705 523194 499567 288551 109942 883658 730020 017999 477350 626634 998799 072459 015709 116235 377832 302087 764225 > 25109 [i]