MinT - Best Known (56, 92, s)-Nets in Base 25

Best Known (56, 92, s)-Nets in Base 25

(56, 92, 326)-Net over F₂₅ — Constructive and digital

Digital (56, 92, 326)-net over F₂₅, using

6 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]

(56, 92, 2757)-Net over F₂₅ — Digital

Digital (56, 92, 2757)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 92, 4394855)-Net in Base 25 — Upper bound on s

There is no (56, 92, 4394856)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 407 832168 962187 808520 279765 131006 473500 867631 747427 067573 771352 616407 139339 720273 739158 556085 153393 361884 779904 885846 655608 657025 > 25⁹² [i]