MinT - Best Known (59, 106, s)-Nets in Base 25

Best Known (59, 106, s)-Nets in Base 25

(59, 106, 326)-Net over F₂₅ — Constructive and digital

Digital (59, 106, 326)-net over F₂₅, using

1 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]

(59, 106, 1271)-Net over F₂₅ — Digital

Digital (59, 106, 1271)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 106, 946541)-Net in Base 25 — Upper bound on s

There is no (59, 106, 946542)-net in base 25, because

1 times m-reduction [i] would yield (59, 105, 946542)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 607 725945 460747 408829 232527 954385 061621 907738 019027 295307 089231 696988 533928 348707 682081 495720 006884 953394 594822 290587 404375 850988 345621 595505 319025 > 25¹⁰⁵ [i]