MinT - Best Known (165, 165+67, s)-Nets in Base 4

Best Known (165, 165+67, s)-Nets in Base 4

(165, 165+67, 531)-Net over F₄ — Constructive and digital

Digital (165, 232, 531)-net over F₄, using

5 times m-reduction [i] based on digital (165, 237, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 79, 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]

(165, 165+67, 1105)-Net over F₄ — Digital

Digital (165, 232, 1105)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+67, 71860)-Net in Base 4 — Upper bound on s

There is no (165, 232, 71861)-net in base 4, because

1 times m-reduction [i] would yield (165, 231, 71861)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 911766 831162 431648 748388 944148 704083 867611 417973 366023 518482 572602 184521 029171 295141 347753 361133 585606 988606 376593 218989 968674 750698 113600 > 4²³¹ [i]