MinT - Best Known (136−38, 136, s)-Nets in Base 4

Best Known (136−38, 136, s)-Nets in Base 4

(136−38, 136, 531)-Net over F₄ — Constructive and digital

Digital (98, 136, 531)-net over F₄, using

4¹ times duplication [i] based on digital (97, 135, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 45, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(136−38, 136, 816)-Net over F₄ — Digital

Digital (98, 136, 816)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−38, 136, 53883)-Net in Base 4 — Upper bound on s

There is no (98, 136, 53884)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7590 902922 176542 355685 700266 749938 337836 746679 404310 987493 748434 592413 966909 083327 > 4¹³⁶ [i]