MinT - Best Known (89−33, 89, s)-Nets in Base 25

Best Known (89−33, 89, s)-Nets in Base 25

(89−33, 89, 356)-Net over F₂₅ — Constructive and digital

Digital (56, 89, 356)-net over F₂₅, using

generalized (u,Â u+v)-construction [i] based on
1. digital (9, 20, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]
2. digital (10, 26, 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]
3. digital (10, 43, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(89−33, 89, 4134)-Net over F₂₅ — Digital

Digital (56, 89, 4134)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−33, 89, large)-Net in Base 25 — Upper bound on s

There is no (56, 89, large)-net in base 25, because

31 times m-reduction [i] would yield (56, 58, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]