MinT - Best Known (56−24, 56, s)-Nets in Base 25

Best Known (56−24, 56, s)-Nets in Base 25

(56−24, 56, 252)-Net over F₂₅ — Constructive and digital

Digital (32, 56, 252)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (10, 22, 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 (10, 34, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(56−24, 56, 1007)-Net over F₂₅ — Digital

Digital (32, 56, 1007)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56−24, 56, 735981)-Net in Base 25 — Upper bound on s

There is no (32, 56, 735982)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1 925957 667312 164479 849939 308689 196075 005452 922809 694427 880532 572200 498925 276225 > 25⁵⁶ [i]