MinT - Best Known (51, 51+41, s)-Nets in Base 5

Best Known (51, 51+41, s)-Nets in Base 5

(51, 51+41, 132)-Net over F₅ — Constructive and digital

Digital (51, 92, 132)-net over F₅, using

2 times m-reduction [i] based on digital (51, 94, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 47, 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]

(51, 51+41, 146)-Net over F₅ — Digital

Digital (51, 92, 146)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+41, 3130)-Net in Base 5 — Upper bound on s

There is no (51, 92, 3131)-net in base 5, because

1 times m-reduction [i] would yield (51, 91, 3131)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4062 584703 971108 306146 375153 747123 095070 311542 445261 785408 920625 > 5⁹¹ [i]