Best Known (88−75, 88, s)-Nets in Base 25
(88−75, 88, 126)-Net over F25 — Constructive and digital
Digital (13, 88, 126)-net over F25, using
- t-expansion [i] based on digital (10, 88, 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
(88−75, 88, 1162)-Net in Base 25 — Upper bound on s
There is no (13, 88, 1163)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 87, 1163)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 41 908687 723501 319496 150725 560103 386634 442774 162276 491377 942519 758687 691631 542737 145928 589207 826345 068755 310087 595633 004329 > 2587 [i]