MinT - Best Known (55−21, 55, s)-Nets in Base 25

Best Known (55−21, 55, s)-Nets in Base 25

(55−21, 55, 252)-Net over F₂₅ — Constructive and digital

Digital (34, 55, 252)-net over F₂₅, using

7 times m-reduction [i] based on digital (34, 62, 252)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 24, 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, 38, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(55−21, 55, 2428)-Net over F₂₅ — Digital

Digital (34, 55, 2428)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(55−21, 55, 6677913)-Net in Base 25 — Upper bound on s

There is no (34, 55, 6677914)-net in base 25, because

1 times m-reduction [i] would yield (34, 54, 6677914)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 3081 490262 354684 280783 095357 230037 450016 989440 666278 746259 050252 100198 523681 > 25⁵⁴ [i]