MinT - Best Known (70, 70+58, s)-Nets in Base 4

Best Known (70, 70+58, s)-Nets in Base 4

(70, 70+58, 130)-Net over F₄ — Constructive and digital

Digital (70, 128, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 64, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(70, 70+58, 134)-Net over F₄ — Digital

Digital (70, 128, 134)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+58, 1743)-Net in Base 4 — Upper bound on s

There is no (70, 128, 1744)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 115804 644983 700896 895894 658599 007766 082556 656731 049930 471306 251378 469912 707524 > 4¹²⁸ [i]