MinT - Best Known (100−41, 100, s)-Nets in Base 25

Best Known (100−41, 100, s)-Nets in Base 25

(100−41, 100, 326)-Net over F₂₅ — Constructive and digital

Digital (59, 100, 326)-net over F₂₅, using

7 times m-reduction [i] based on digital (59, 107, 326)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 34, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
        the Hermitian function field over F₂₅ [i]
  2. digital (25, 73, 200)-net over F₂₅, using
    - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
        a function field by GarcÃa and Quoos [i]

(100−41, 100, 2073)-Net over F₂₅ — Digital

Digital (59, 100, 2073)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−41, 100, 2876712)-Net in Base 25 — Upper bound on s

There is no (59, 100, 2876713)-net in base 25, because

1 times m-reduction [i] would yield (59, 99, 2876713)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2 489213 436019 213642 149087 181624 500634 731416 370226 217763 988125 254877 083061 404836 274483 252858 657345 512273 224103 332197 741615 210287 185737 630305 > 25⁹⁹ [i]