MinT - Best Known (86−40, 86, s)-Nets in Base 4

Best Known (86−40, 86, s)-Nets in Base 4

(86−40, 86, 76)-Net over F₄ — Constructive and digital

Digital (46, 86, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 43, 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]

(86−40, 86, 90)-Net over F₄ — Digital

Digital (46, 86, 90)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−40, 86, 1058)-Net in Base 4 — Upper bound on s

There is no (46, 86, 1059)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6096 247789 218894 920889 987432 053835 595763 040145 121944 > 4⁸⁶ [i]