MinT - Best Known (42, 42+36, s)-Nets in Base 4

Best Known (42, 42+36, s)-Nets in Base 4

(42, 42+36, 76)-Net over F₄ — Constructive and digital

Digital (42, 78, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 39, 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]

(42, 42+36, 85)-Net over F₄ — Digital

Digital (42, 78, 85)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+36, 1008)-Net in Base 4 — Upper bound on s

There is no (42, 78, 1009)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 91795 039806 403321 783742 270966 695976 949675 502816 > 4⁷⁸ [i]