MinT - Best Known (80−38, 80, s)-Nets in Base 4

Best Known (80−38, 80, s)-Nets in Base 4

(80−38, 80, 66)-Net over F₄ — Constructive and digital

Digital (42, 80, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 40, 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]

(80−38, 80, 79)-Net over F₄ — Digital

Digital (42, 80, 79)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(80−38, 80, 890)-Net in Base 4 — Upper bound on s

There is no (42, 80, 891)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 471546 160212 036148 937223 299902 865548 532042 579412 > 4⁸⁰ [i]