Best Known (81−66, 81, s)-Nets in Base 25
(81−66, 81, 126)-Net over F25 — Constructive and digital
Digital (15, 81, 126)-net over F25, using
- t-expansion [i] based on digital (10, 81, 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
(81−66, 81, 140)-Net over F25 — Digital
Digital (15, 81, 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
(81−66, 81, 1463)-Net in Base 25 — Upper bound on s
There is no (15, 81, 1464)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 173694 483743 644471 726145 005945 019610 958937 400180 762026 635198 460921 445472 299703 970361 071607 807675 818787 054040 588609 > 2581 [i]