MinT - Best Known (67, 67+57, s)-Nets in Base 5

Best Known (67, 67+57, s)-Nets in Base 5

(67, 67+57, 132)-Net over F₅ — Constructive and digital

Digital (67, 124, 132)-net over F₅, using

2 times m-reduction [i] based on digital (67, 126, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 63, 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]

(67, 67+57, 165)-Net over F₅ — Digital

Digital (67, 124, 165)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+57, 3301)-Net in Base 5 — Upper bound on s

There is no (67, 124, 3302)-net in base 5, because

1 times m-reduction [i] would yield (67, 123, 3302)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 94 274249 819013 262235 761144 848338 139706 055312 287725 749383 090915 442755 423306 202126 892225 > 5¹²³ [i]