MinT - Best Known (88−40, 88, s)-Nets in Base 4

Best Known (88−40, 88, s)-Nets in Base 4

(88−40, 88, 90)-Net over F₄ — Constructive and digital

Digital (48, 88, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 44, 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]

(88−40, 88, 98)-Net over F₄ — Digital

Digital (48, 88, 98)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−40, 88, 1217)-Net in Base 4 — Upper bound on s

There is no (48, 88, 1218)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 96206 447042 419567 470250 027818 214550 599361 438036 308624 > 4⁸⁸ [i]