MinT - Best Known (47, 86, s)-Nets in Base 4

Best Known (47, 86, s)-Nets in Base 4

(47, 86, 90)-Net over F₄ — Constructive and digital

Digital (47, 86, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 43, 45)-net over F₁₆, using
- net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]

(47, 86, 97)-Net over F₄ — Digital

Digital (47, 86, 97)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 86, 1289)-Net in Base 4 — Upper bound on s

There is no (47, 86, 1290)-net in base 4, because

1 times m-reduction [i] would yield (47, 85, 1290)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1508 267125 631224 412407 205247 236838 257437 393204 279360 > 4⁸⁵ [i]