Best Known (81−69, 81, s)-Nets in Base 25
(81−69, 81, 126)-Net over F25 — Constructive and digital
Digital (12, 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
(81−69, 81, 1079)-Net in Base 25 — Upper bound on s
There is no (12, 81, 1080)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 80, 1080)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 6846 863850 536374 295061 386832 511431 535437 848796 942735 669038 645066 763783 139895 105975 567919 858142 861235 557787 781505 > 2580 [i]