MinT - Best Known (55, 55+39, s)-Nets in Base 5

Best Known (55, 55+39, s)-Nets in Base 5

(55, 55+39, 132)-Net over F₅ — Constructive and digital

Digital (55, 94, 132)-net over F₅, using

8 times m-reduction [i] based on digital (55, 102, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 51, 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]

(55, 55+39, 190)-Net over F₅ — Digital

Digital (55, 94, 190)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+39, 5215)-Net in Base 5 — Upper bound on s

There is no (55, 94, 5216)-net in base 5, because

1 times m-reduction [i] would yield (55, 93, 5216)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 101195 741220 226940 600981 235049 637858 284411 336346 965309 222859 863425 > 5⁹³ [i]