MinT - Best Known (86−31, 86, s)-Nets in Base 25

Best Known (86−31, 86, s)-Nets in Base 25

(86−31, 86, 378)-Net over F₂₅ — Constructive and digital

Digital (55, 86, 378)-net over F₂₅, using

generalized (u,Â u+v)-construction [i] based on
1. digital (10, 20, 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, 25, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)
3. digital (10, 41, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(86−31, 86, 5120)-Net over F₂₅ — Digital

Digital (55, 86, 5120)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−31, 86, large)-Net in Base 25 — Upper bound on s

There is no (55, 86, large)-net in base 25, because

29 times m-reduction [i] would yield (55, 57, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]