MinT - Best Known (70, 70+64, s)-Nets in Base 4

Best Known (70, 70+64, s)-Nets in Base 4

(70, 70+64, 76)-Net over F₄ — Constructive and digital

Digital (70, 134, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 67, 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, 70+64, 118)-Net over F₄ — Digital

Digital (70, 134, 118)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+64, 1389)-Net in Base 4 — Upper bound on s

There is no (70, 134, 1390)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 480 355250 574848 112268 717983 558489 420937 909177 997631 590899 037137 758053 812432 295635 > 4¹³⁴ [i]