MinT - Best Known (55−23, 55, s)-Nets in Base 25

Best Known (55−23, 55, s)-Nets in Base 25

(55−23, 55, 252)-Net over F₂₅ — Constructive and digital

Digital (32, 55, 252)-net over F₂₅, using

1 times m-reduction [i] based on 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)

(55−23, 55, 1190)-Net over F₂₅ — Digital

Digital (32, 55, 1190)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(55−23, 55, 1490788)-Net in Base 25 — Upper bound on s

There is no (32, 55, 1490789)-net in base 25, because

1 times m-reduction [i] would yield (32, 54, 1490789)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 3081 508765 795565 560864 878965 410481 600583 872771 087868 670658 449524 742464 620137 > 25⁵⁴ [i]