MinT - Best Known (134, 134+101, s)-Nets in Base 4

Best Known (134, 134+101, s)-Nets in Base 4

(134, 134+101, 131)-Net over F₄ — Constructive and digital

Digital (134, 235, 131)-net over F₄, using

1 times m-reduction [i] based on digital (134, 236, 131)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 61, 27)-net over F₄, using
    - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
        an explicitly constructive algebraic function field [i]
  2. digital (73, 175, 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]

(134, 134+101, 267)-Net over F₄ — Digital

Digital (134, 235, 267)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 134+101, 4226)-Net in Base 4 — Upper bound on s

There is no (134, 235, 4227)-net in base 4, because

1 times m-reduction [i] would yield (134, 234, 4227)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 766 103138 041676 627909 171393 659589 572856 618615 404337 745463 140754 484886 286481 572774 465300 447497 664170 777020 181126 653279 345892 873724 748624 641096 > 4²³⁴ [i]