MinT - Best Known (51, 51+37, s)-Nets in Base 5

Best Known (51, 51+37, s)-Nets in Base 5

(51, 51+37, 132)-Net over F₅ — Constructive and digital

Digital (51, 88, 132)-net over F₅, using

6 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+37, 172)-Net over F₅ — Digital

Digital (51, 88, 172)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+37, 4499)-Net in Base 5 — Upper bound on s

There is no (51, 88, 4500)-net in base 5, because

1 times m-reduction [i] would yield (51, 87, 4500)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6 472787 395412 022858 413424 785851 843017 630573 858147 577364 017601 > 5⁸⁷ [i]