MinT - Best Known (57−22, 57, s)-Nets in Base 25

Best Known (57−22, 57, s)-Nets in Base 25

(57−22, 57, 252)-Net over F₂₅ — Constructive and digital

Digital (35, 57, 252)-net over F₂₅, using

8 times m-reduction [i] based on digital (35, 65, 252)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 25, 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, 40, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(57−22, 57, 2263)-Net over F₂₅ — Digital

Digital (35, 57, 2263)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(57−22, 57, 3586519)-Net in Base 25 — Upper bound on s

There is no (35, 57, 3586520)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 48 148308 909500 364655 809511 212653 129318 116473 250360 705765 304975 791628 678518 137793 > 25⁵⁷ [i]