MinT - Best Known (239−70, 239, s)-Nets in Base 4

Best Known (239−70, 239, s)-Nets in Base 4

(239−70, 239, 531)-Net over F₄ — Constructive and digital

Digital (169, 239, 531)-net over F₄, using

4 times m-reduction [i] based on digital (169, 243, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 81, 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]

(239−70, 239, 1067)-Net over F₄ — Digital

Digital (169, 239, 1067)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−70, 239, 59861)-Net in Base 4 — Upper bound on s

There is no (169, 239, 59862)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 780872 430553 733513 112259 272051 120317 570666 926221 992671 318558 640560 355805 248243 452013 993135 436641 253342 009923 286637 379439 955252 585806 684486 101188 > 4²³⁹ [i]