MinT - Best Known (57, 57+33, s)-Nets in Base 5

Best Known (57, 57+33, s)-Nets in Base 5

(57, 57+33, 252)-Net over F₅ — Constructive and digital

Digital (57, 90, 252)-net over F₅, using

4 times m-reduction [i] based on digital (57, 94, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 47, 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]

(57, 57+33, 297)-Net over F₅ — Digital

Digital (57, 90, 297)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+33, 13125)-Net in Base 5 — Upper bound on s

There is no (57, 90, 13126)-net in base 5, because

1 times m-reduction [i] would yield (57, 89, 13126)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 161 637451 839429 503912 414470 180518 628871 461584 789994 788985 210625 > 5⁸⁹ [i]