MinT - Best Known (56, 56+37, s)-Nets in Base 5

Best Known (56, 56+37, s)-Nets in Base 5

(56, 56+37, 208)-Net over F₅ — Constructive and digital

Digital (56, 93, 208)-net over F₅, using

1 times m-reduction [i] based on digital (56, 94, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 47, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

(56, 56+37, 220)-Net over F₅ — Digital

Digital (56, 93, 220)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+37, 7043)-Net in Base 5 — Upper bound on s

There is no (56, 93, 7044)-net in base 5, because

1 times m-reduction [i] would yield (56, 92, 7044)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 20225 130301 185423 460671 614788 316758 236672 279946 002757 964434 326721 > 5⁹² [i]