MinT - Best Known (119−55, 119, s)-Nets in Base 5

Best Known (119−55, 119, s)-Nets in Base 5

(119−55, 119, 132)-Net over F₅ — Constructive and digital

Digital (64, 119, 132)-net over F₅, using

1 times m-reduction [i] based on digital (64, 120, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 60, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(119−55, 119, 157)-Net over F₅ — Digital

Digital (64, 119, 157)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−55, 119, 3078)-Net in Base 5 — Upper bound on s

There is no (64, 119, 3079)-net in base 5, because

1 times m-reduction [i] would yield (64, 118, 3079)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 30234 521069 329195 578081 076973 832634 322446 308734 042293 556705 272809 567798 671834 347061 > 5¹¹⁸ [i]