MinT - Best Known (51, 51+43, s)-Nets in Base 5

Best Known (51, 51+43, s)-Nets in Base 5

(51, 51+43, 132)-Net over F₅ — Constructive and digital

Digital (51, 94, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 47, 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]

(51, 51+43, 135)-Net over F₅ — Digital

Digital (51, 94, 135)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+43, 2687)-Net in Base 5 — Upper bound on s

There is no (51, 94, 2688)-net in base 5, because

1 times m-reduction [i] would yield (51, 93, 2688)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 101023 369975 703233 879044 051496 826588 128099 621011 227279 485022 288385 > 5⁹³ [i]