MinT - Best Known (57, 57+47, s)-Nets in Base 5

Best Known (57, 57+47, s)-Nets in Base 5

(57, 57+47, 132)-Net over F₅ — Constructive and digital

Digital (57, 104, 132)-net over F₅, using

2 times m-reduction [i] based on digital (57, 106, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 53, 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]

(57, 57+47, 152)-Net over F₅ — Digital

Digital (57, 104, 152)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+47, 3164)-Net in Base 5 — Upper bound on s

There is no (57, 104, 3165)-net in base 5, because

1 times m-reduction [i] would yield (57, 103, 3165)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 991071 810816 901528 886519 261647 155201 657212 681044 148361 049006 662558 297885 > 5¹⁰³ [i]