MinT - Best Known (38, 38+38, s)-Nets in Base 25

Best Known (38, 38+38, s)-Nets in Base 25

(38, 38+38, 230)-Net over F₂₅ — Constructive and digital

Digital (38, 76, 230)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (9, 28, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]
2. digital (10, 48, 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]

(38, 38+38, 470)-Net over F₂₅ — Digital

Digital (38, 76, 470)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+38, 129042)-Net in Base 25 — Upper bound on s

There is no (38, 76, 129043)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 17518 609382 313835 160859 414985 029692 084266 750893 581698 463616 087538 536413 624688 125724 518695 014627 445742 836825 > 25⁷⁶ [i]