MinT - Best Known (70−32, 70, s)-Nets in Base 4

Best Known (70−32, 70, s)-Nets in Base 4

(70−32, 70, 76)-Net over F₄ — Constructive and digital

Digital (38, 70, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 35, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(70−32, 70, 81)-Net over F₄ — Digital

Digital (38, 70, 81)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−32, 70, 963)-Net in Base 4 — Upper bound on s

There is no (38, 70, 964)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 412489 637450 720138 707781 743759 802841 587460 > 4⁷⁰ [i]