MinT - Best Known (84−40, 84, s)-Nets in Base 4

Best Known (84−40, 84, s)-Nets in Base 4

(84−40, 84, 66)-Net over F₄ — Constructive and digital

Digital (44, 84, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 42, 33)-net over F₁₆, using
- net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]

(84−40, 84, 82)-Net over F₄ — Digital

Digital (44, 84, 82)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−40, 84, 918)-Net in Base 4 — Upper bound on s

There is no (44, 84, 919)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 374 184404 858236 128181 944069 536278 850834 983458 257839 > 4⁸⁴ [i]