MinT - Best Known (141−55, 141, s)-Nets in Base 5

Best Known (141−55, 141, s)-Nets in Base 5

(141−55, 141, 252)-Net over F₅ — Constructive and digital

Digital (86, 141, 252)-net over F₅, using

t-expansion [i] based on digital (85, 141, 252)-net over F₅, using
- 9 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]

(141−55, 141, 333)-Net over F₅ — Digital

Digital (86, 141, 333)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−55, 141, 11478)-Net in Base 5 — Upper bound on s

There is no (86, 141, 11479)-net in base 5, because

1 times m-reduction [i] would yield (86, 140, 11479)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 811108 080880 005521 832548 888130 574490 823760 788781 431759 822844 179171 768003 520621 593780 466390 877813 > 5¹⁴⁰ [i]