MinT - Best Known (82−38, 82, s)-Nets in Base 4

Best Known (82−38, 82, s)-Nets in Base 4

(82−38, 82, 76)-Net over F₄ — Constructive and digital

Digital (44, 82, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 41, 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]

(82−38, 82, 87)-Net over F₄ — Digital

Digital (44, 82, 87)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(82−38, 82, 1032)-Net in Base 4 — Upper bound on s

There is no (44, 82, 1033)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23 389420 608890 488057 120316 134587 880222 619468 098048 > 4⁸² [i]