MinT - Best Known (72−32, 72, s)-Nets in Base 4

Best Known (72−32, 72, s)-Nets in Base 4

(72−32, 72, 90)-Net over F₄ — Constructive and digital

Digital (40, 72, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 36, 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]

(72−32, 72, 91)-Net over F₄ — Digital

Digital (40, 72, 91)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−32, 72, 1147)-Net in Base 4 — Upper bound on s

There is no (40, 72, 1148)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 22 351691 829515 086809 241648 215875 053546 101685 > 4⁷² [i]