MinT - Best Known (96−45, 96, s)-Nets in Base 4

Best Known (96−45, 96, s)-Nets in Base 4

(96−45, 96, 76)-Net over F₄ — Constructive and digital

Digital (51, 96, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 48, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(96−45, 96, 96)-Net over F₄ — Digital

Digital (51, 96, 96)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(96−45, 96, 1183)-Net in Base 4 — Upper bound on s

There is no (51, 96, 1184)-net in base 4, because

1 times m-reduction [i] would yield (51, 95, 1184)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1590 992940 227776 714870 896320 369776 869722 229375 998615 377555 > 4⁹⁵ [i]