MinT - Best Known (74−25, 74, s)-Nets in Base 5

Best Known (74−25, 74, s)-Nets in Base 5

(74−25, 74, 252)-Net over F₅ — Constructive and digital

Digital (49, 74, 252)-net over F₅, using

4 times m-reduction [i] based on digital (49, 78, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 39, 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]

(74−25, 74, 362)-Net over F₅ — Digital

Digital (49, 74, 362)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(74−25, 74, 23616)-Net in Base 5 — Upper bound on s

There is no (49, 74, 23617)-net in base 5, because

1 times m-reduction [i] would yield (49, 73, 23617)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1059 143452 269562 909290 207878 106106 118736 348318 339665 > 5⁷³ [i]