MinT - Best Known (84−38, 84, s)-Nets in Base 4

Best Known (84−38, 84, s)-Nets in Base 4

(84−38, 84, 90)-Net over F₄ — Constructive and digital

Digital (46, 84, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 42, 45)-net over F₁₆, using
- net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]

(84−38, 84, 96)-Net over F₄ — Digital

Digital (46, 84, 96)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−38, 84, 1197)-Net in Base 4 — Upper bound on s

There is no (46, 84, 1198)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 376 118627 456732 381576 402545 568678 655841 402285 361236 > 4⁸⁴ [i]