MinT - Best Known (70−47, 70, s)-Nets in Base 25

Best Known (70−47, 70, s)-Nets in Base 25

(70−47, 70, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 70, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 70, 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]

(70−47, 70, 176)-Net over F₂₅ — Digital

Digital (23, 70, 176)-net over F₂₅, using

net from sequence [i] based on digital (23, 175)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 23 and N(F) ≥ 176, using
  - an algebraic function field by Teo [i]

(70−47, 70, 6126)-Net in Base 25 — Upper bound on s

There is no (23, 70, 6127)-net in base 25, because

1 times m-reduction [i] would yield (23, 69, 6127)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2 874307 080035 415565 274786 425992 088759 332605 946747 437158 126828 697283 355259 779693 901527 395289 953625 > 25⁶⁹ [i]