Best Known (59−35, 59, s)-Nets in Base 25
(59−35, 59, 148)-Net over F25 — Constructive and digital
Digital (24, 59, 148)-net over F25, using
- t-expansion [i] based on digital (19, 59, 148)-net over F25, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 148, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
(59−35, 59, 184)-Net over F25 — Digital
Digital (24, 59, 184)-net over F25, using
- net from sequence [i] based on digital (24, 183)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 24 and N(F) ≥ 184, using
(59−35, 59, 17577)-Net in Base 25 — Upper bound on s
There is no (24, 59, 17578)-net in base 25, because
- 1 times m-reduction [i] would yield (24, 58, 17578)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1204 092094 968717 065976 685540 477712 517001 116822 032958 603598 095190 704268 672693 423345 > 2558 [i]