MinT - Best Known (38, 38+22, s)-Nets in Base 25

Best Known (38, 38+22, s)-Nets in Base 25

(38, 38+22, 278)-Net over F₂₅ — Constructive and digital

Digital (38, 60, 278)-net over F₂₅, using

1 times m-reduction [i] based on digital (38, 61, 278)-net over F₂₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 7, 26)-net over F₂₅, using
    - net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
      - Niederreiter sequence [i]
  2. 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]
  3. digital (10, 33, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(38, 38+22, 3578)-Net over F₂₅ — Digital

Digital (38, 60, 3578)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+22, large)-Net in Base 25 — Upper bound on s

There is no (38, 60, large)-net in base 25, because

20 times m-reduction [i] would yield (38, 40, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]