MinT - Best Known (54, 54+41, s)-Nets in Base 5

Best Known (54, 54+41, s)-Nets in Base 5

(54, 54+41, 132)-Net over F₅ — Constructive and digital

Digital (54, 95, 132)-net over F₅, using

5 times m-reduction [i] based on digital (54, 100, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 50, 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]

(54, 54+41, 167)-Net over F₅ — Digital

Digital (54, 95, 167)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+41, 3988)-Net in Base 5 — Upper bound on s

There is no (54, 95, 3989)-net in base 5, because

1 times m-reduction [i] would yield (54, 94, 3989)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 505627 577096 786432 258310 682013 411562 117419 268736 799461 294083 327665 > 5⁹⁴ [i]