MinT - Best Known (239−72, 239, s)-Nets in Base 4

Best Known (239−72, 239, s)-Nets in Base 4

(239−72, 239, 531)-Net over F₄ — Constructive and digital

Digital (167, 239, 531)-net over F₄, using

1 times m-reduction [i] based on digital (167, 240, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 80, 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]

(239−72, 239, 950)-Net over F₄ — Digital

Digital (167, 239, 950)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−72, 239, 47244)-Net in Base 4 — Upper bound on s

There is no (167, 239, 47245)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 780544 516404 808255 562484 213773 718388 626731 535487 064361 407949 925384 225080 818391 203497 827531 665156 644717 849171 560592 119101 628510 108336 637566 563380 > 4²³⁹ [i]