MinT - Best Known (67, 67+59, s)-Nets in Base 5

Best Known (67, 67+59, s)-Nets in Base 5

(67, 67+59, 132)-Net over F₅ — Constructive and digital

Digital (67, 126, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 63, 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]

(67, 67+59, 157)-Net over F₅ — Digital

Digital (67, 126, 157)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+59, 2983)-Net in Base 5 — Upper bound on s

There is no (67, 126, 2984)-net in base 5, because

1 times m-reduction [i] would yield (67, 125, 2984)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2352 412859 723118 180077 556927 107168 179478 135734 338479 679863 979653 334955 825565 483190 008225 > 5¹²⁵ [i]