MinT - Best Known (95−39, 95, s)-Nets in Base 25

Best Known (95−39, 95, s)-Nets in Base 25

(95−39, 95, 326)-Net over F₂₅ — Constructive and digital

Digital (56, 95, 326)-net over F₂₅, using

3 times m-reduction [i] based on digital (56, 98, 326)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 31, 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, 67, 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]

(95−39, 95, 1975)-Net over F₂₅ — Digital

Digital (56, 95, 1975)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−39, 95, 2723497)-Net in Base 25 — Upper bound on s

There is no (56, 95, 2723498)-net in base 25, because

1 times m-reduction [i] would yield (56, 94, 2723498)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 254895 865329 250406 396171 203376 223256 986765 339609 917375 035109 589221 114984 067983 422527 343856 041764 430121 273437 491875 956984 393901 677585 > 25⁹⁴ [i]