MinT - Best Known (82−36, 82, s)-Nets in Base 4

Best Known (82−36, 82, s)-Nets in Base 4

(82−36, 82, 98)-Net over F₄ — Constructive and digital

Digital (46, 82, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 41, 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]

(82−36, 82, 104)-Net over F₄ — Digital

Digital (46, 82, 104)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(82−36, 82, 1377)-Net in Base 4 — Upper bound on s

There is no (46, 82, 1378)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23 433035 376398 395138 743376 608339 344363 989062 119200 > 4⁸² [i]