MinT - Best Known (143, 256, s)-Nets in Base 4

Best Known (143, 256, s)-Nets in Base 4

(143, 256, 134)-Net over F₄ — Constructive and digital

Digital (143, 256, 134)-net over F₄, using

1 times m-reduction [i] based on digital (143, 257, 134)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 70, 30)-net over F₄, using
    - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
        F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
  2. digital (73, 187, 104)-net over F₄, using
    - net from sequence [i] based on digital (73, 103)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
        F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(143, 256, 265)-Net over F₄ — Digital

Digital (143, 256, 265)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 256, 3944)-Net in Base 4 — Upper bound on s

There is no (143, 256, 3945)-net in base 4, because

1 times m-reduction [i] would yield (143, 255, 3945)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3367 263892 530818 622914 056451 756433 568901 472438 269395 348807 120269 766448 821538 314378 622747 009242 743708 602743 312486 717759 935099 649559 029647 362736 050105 515444 > 4²⁵⁵ [i]