MinT - Best Known (59−23, 59, s)-Nets in Base 5

Best Known (59−23, 59, s)-Nets in Base 5

(59−23, 59, 132)-Net over F₅ — Constructive and digital

Digital (36, 59, 132)-net over F₅, using

5 times m-reduction [i] based on digital (36, 64, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 32, 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]

(59−23, 59, 173)-Net over F₅ — Digital

Digital (36, 59, 173)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(59−23, 59, 5941)-Net in Base 5 — Upper bound on s

There is no (36, 59, 5942)-net in base 5, because

1 times m-reduction [i] would yield (36, 58, 5942)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 34752 582943 047348 257909 055250 775571 129337 > 5⁵⁸ [i]