MinT - Best Known (39, 39+27, s)-Nets in Base 25

Best Known (39, 39+27, s)-Nets in Base 25

(39, 39+27, 252)-Net over F₂₅ — Constructive and digital

Digital (39, 66, 252)-net over F₂₅, using

11 times m-reduction [i] based on digital (39, 77, 252)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 29, 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, 48, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(39, 39+27, 1568)-Net over F₂₅ — Digital

Digital (39, 66, 1568)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+27, 2306182)-Net in Base 25 — Upper bound on s

There is no (39, 66, 2306183)-net in base 25, because

1 times m-reduction [i] would yield (39, 65, 2306183)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 7 346843 759525 951673 197838 863920 394082 311306 978810 280139 578612 335117 997950 818568 218320 332425 > 25⁶⁵ [i]