MinT - Best Known (107−40, 107, s)-Nets in Base 25

Best Known (107−40, 107, s)-Nets in Base 25

(107−40, 107, 378)-Net over F₂₅ — Constructive and digital

Digital (67, 107, 378)-net over F₂₅, using

t-expansion [i] based on digital (66, 107, 378)-net over F₂₅, using
- 3 times m-reduction [i] based on digital (66, 110, 378)-net over F₂₅, using
  - generalized (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, 32, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)
    3. digital (10, 54, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(107−40, 107, 4411)-Net over F₂₅ — Digital

Digital (67, 107, 4411)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−40, 107, large)-Net in Base 25 — Upper bound on s

There is no (67, 107, large)-net in base 25, because

38 times m-reduction [i] would yield (67, 69, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]