Best Known (89−75, 89, s)-Nets in Base 25
(89−75, 89, 126)-Net over F25 — Constructive and digital
Digital (14, 89, 126)-net over F25, using
- t-expansion [i] based on digital (10, 89, 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
(89−75, 89, 130)-Net over F25 — Digital
Digital (14, 89, 130)-net over F25, using
- net from sequence [i] based on digital (14, 129)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 14 and N(F) ≥ 130, using
(89−75, 89, 1270)-Net in Base 25 — Upper bound on s
There is no (14, 89, 1271)-net in base 25, because
- 1 times m-reduction [i] would yield (14, 88, 1271)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1063 697180 954374 801602 534664 564220 802552 448691 956605 393026 554248 933768 964815 172043 034713 581806 747015 111346 068023 456820 519625 > 2588 [i]