MinT - Best Known (69−47, 69, s)-Nets in Base 25

Best Known (69−47, 69, s)-Nets in Base 25

(69−47, 69, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 69, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 69, 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]

(69−47, 69, 171)-Net over F₂₅ — Digital

Digital (22, 69, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 69, 171)-net over F₂₅, using
- net from sequence [i] based on digital (20, 170)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 20 and N(F) ≥ 171, using
    - an algebraic function field by Teo [i]

(69−47, 69, 5324)-Net in Base 25 — Upper bound on s

There is no (22, 69, 5325)-net in base 25, because

1 times m-reduction [i] would yield (22, 68, 5325)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 114844 513077 897982 402004 044410 755126 961991 122976 332504 439525 949824 405934 283540 522789 450509 113801 > 25⁶⁸ [i]