MinT - Best Known (89−32, 89, s)-Nets in Base 25

Best Known (89−32, 89, s)-Nets in Base 25

(89−32, 89, 378)-Net over F₂₅ — Constructive and digital

Digital (57, 89, 378)-net over F₂₅, using

1 times m-reduction [i] based on digital (57, 90, 378)-net over F₂₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (10, 21, 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, 26, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)
  3. digital (10, 43, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(89−32, 89, 5352)-Net over F₂₅ — Digital

Digital (57, 89, 5352)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−32, 89, large)-Net in Base 25 — Upper bound on s

There is no (57, 89, large)-net in base 25, because

30 times m-reduction [i] would yield (57, 59, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]