Best Known (87−75, 87, s)-Nets in Base 25
(87−75, 87, 126)-Net over F25 — Constructive and digital
Digital (12, 87, 126)-net over F25, using
- t-expansion [i] based on digital (10, 87, 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
(87−75, 87, 1064)-Net in Base 25 — Upper bound on s
There is no (12, 87, 1065)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 86, 1065)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1 706164 170291 047146 806975 092409 879101 941502 282132 319859 909409 960193 555620 704233 460428 499886 153243 606875 408557 910366 857913 > 2586 [i]