MinT - Best Known (58, 58+41, s)-Nets in Base 25

Best Known (58, 58+41, s)-Nets in Base 25

(58, 58+41, 326)-Net over F₂₅ — Constructive and digital

Digital (58, 99, 326)-net over F₂₅, using

5 times m-reduction [i] based on digital (58, 104, 326)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 33, 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, 71, 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]

(58, 58+41, 1914)-Net over F₂₅ — Digital

Digital (58, 99, 1914)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+41, 2449058)-Net in Base 25 — Upper bound on s

There is no (58, 99, 2449059)-net in base 25, because

1 times m-reduction [i] would yield (58, 98, 2449059)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 99568 467201 473384 729080 503602 811156 851230 632962 151517 465305 188459 662563 995204 801731 437214 991259 616001 248947 783023 312071 798286 685082 156705 > 25⁹⁸ [i]