MinT - Best Known (86−38, 86, s)-Nets in Base 4

Best Known (86−38, 86, s)-Nets in Base 4

(86−38, 86, 98)-Net over F₄ — Constructive and digital

Digital (48, 86, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 43, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(86−38, 86, 105)-Net over F₄ — Digital

Digital (48, 86, 105)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−38, 86, 1388)-Net in Base 4 — Upper bound on s

There is no (48, 86, 1389)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6050 126353 811590 047305 322611 867637 725847 453655 761160 > 4⁸⁶ [i]