MinT - Best Known (53, 53+37, s)-Nets in Base 5

Best Known (53, 53+37, s)-Nets in Base 5

(53, 53+37, 132)-Net over F₅ — Constructive and digital

Digital (53, 90, 132)-net over F₅, using

8 times m-reduction [i] based on digital (53, 98, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 49, 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]

(53, 53+37, 190)-Net over F₅ — Digital

Digital (53, 90, 190)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+37, 5383)-Net in Base 5 — Upper bound on s

There is no (53, 90, 5384)-net in base 5, because

1 times m-reduction [i] would yield (53, 89, 5384)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 161 981689 269303 817886 112444 667061 831291 111693 709183 029604 471425 > 5⁸⁹ [i]