MinT - Best Known (99−75, 99, s)-Nets in Base 25

Best Known (99−75, 99, s)-Nets in Base 25

(99−75, 99, 148)-Net over F₂₅ — Constructive and digital

Digital (24, 99, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 99, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(99−75, 99, 184)-Net over F₂₅ — Digital

Digital (24, 99, 184)-net over F₂₅, using

net from sequence [i] based on digital (24, 183)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 24 and N(F) ≥ 184, using
  - an algebraic function field by Teo [i]

(99−75, 99, 3059)-Net in Base 25 — Upper bound on s

There is no (24, 99, 3060)-net in base 25, because

1 times m-reduction [i] would yield (24, 98, 3060)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 100674 350634 000421 452699 314550 466804 925571 783145 579198 615040 157555 284276 238023 245628 184594 124453 844254 439756 279320 072129 045786 184548 117345 > 25⁹⁸ [i]