MinT - Best Known (56, 56+49, s)-Nets in Base 5

Best Known (56, 56+49, s)-Nets in Base 5

(56, 56+49, 104)-Net over F₅ — Constructive and digital

Digital (56, 105, 104)-net over F₅, using

1 times m-reduction [i] based on digital (56, 106, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 53, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(56, 56+49, 137)-Net over F₅ — Digital

Digital (56, 105, 137)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+49, 2601)-Net in Base 5 — Upper bound on s

There is no (56, 105, 2602)-net in base 5, because

1 times m-reduction [i] would yield (56, 104, 2602)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 940932 542024 783310 140177 200825 431944 270298 251317 091920 827765 318842 615425 > 5¹⁰⁴ [i]