MinT - Best Known (51, 96, s)-Nets in Base 5

Best Known (51, 96, s)-Nets in Base 5

(51, 96, 104)-Net over F₅ — Constructive and digital

Digital (51, 96, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 48, 52)-net over F₂₅, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by GarcÃa and Quoos [i]

(51, 96, 125)-Net over F₅ — Digital

Digital (51, 96, 125)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 96, 2344)-Net in Base 5 — Upper bound on s

There is no (51, 96, 2345)-net in base 5, because

1 times m-reduction [i] would yield (51, 95, 2345)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 526429 736178 701073 778747 278380 386842 877392 959763 376322 809282 154185 > 5⁹⁵ [i]