MinT - Best Known (110−86, 110, s)-Nets in Base 25

Best Known (110−86, 110, s)-Nets in Base 25

(110−86, 110, 148)-Net over F₂₅ — Constructive and digital

Digital (24, 110, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 110, 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]

(110−86, 110, 184)-Net over F₂₅ — Digital

Digital (24, 110, 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]

(110−86, 110, 2628)-Net in Base 25 — Upper bound on s

There is no (24, 110, 2629)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 6023 140397 056483 593191 644902 147306 659996 604978 482199 277377 531068 239870 170021 728674 439455 399078 105593 672660 393127 954274 996192 516122 154865 143606 110100 792425 > 25¹¹⁰ [i]