MinT - Best Known (134, 134+102, s)-Nets in Base 4

Best Known (134, 134+102, s)-Nets in Base 4

(134, 134+102, 131)-Net over F₄ — Constructive and digital

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+102, 264)-Net over F₄ — Digital

Digital (134, 236, 264)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 134+102, 4001)-Net in Base 4 — Upper bound on s

There is no (134, 236, 4002)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12274 344419 084656 727208 328001 129555 387693 870764 954788 448078 377836 201750 499940 749915 467188 631282 124102 772739 207546 095529 462556 709061 993787 556672 > 4²³⁶ [i]