MinT - Best Known (57, 57+29, s)-Nets in Base 5

Best Known (57, 57+29, s)-Nets in Base 5

(57, 57+29, 252)-Net over F₅ — Constructive and digital

Digital (57, 86, 252)-net over F₅, using

8 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+29, 410)-Net over F₅ — Digital

Digital (57, 86, 410)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+29, 26483)-Net in Base 5 — Upper bound on s

There is no (57, 86, 26484)-net in base 5, because

1 times m-reduction [i] would yield (57, 85, 26484)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 258521 494300 192219 037065 439317 196377 145644 412634 893437 452225 > 5⁸⁵ [i]