MinT - Best Known (140−55, 140, s)-Nets in Base 5

Best Known (140−55, 140, s)-Nets in Base 5

(140−55, 140, 252)-Net over F₅ — Constructive and digital

Digital (85, 140, 252)-net over F₅, using

10 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 75, 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]

(140−55, 140, 322)-Net over F₅ — Digital

Digital (85, 140, 322)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−55, 140, 10813)-Net in Base 5 — Upper bound on s

There is no (85, 140, 10814)-net in base 5, because

1 times m-reduction [i] would yield (85, 139, 10814)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14 376423 477778 546101 017449 577544 043829 266584 585678 199592 605217 918224 027524 375829 870991 374589 832729 > 5¹³⁹ [i]