MinT - Best Known (239−71, 239, s)-Nets in Base 4

Best Known (239−71, 239, s)-Nets in Base 4

(239−71, 239, 531)-Net over F₄ — Constructive and digital

Digital (168, 239, 531)-net over F₄, using

t-expansion [i] based on 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]

(239−71, 239, 1006)-Net over F₄ — Digital

Digital (168, 239, 1006)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−71, 239, 57535)-Net in Base 4 — Upper bound on s

There is no (168, 239, 57536)-net in base 4, because

1 times m-reduction [i] would yield (168, 238, 57536)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 195195 417028 096804 391639 950910 510839 950489 573076 636022 609785 028181 957226 596230 302485 169215 880170 690343 982457 781943 506344 279997 740770 553345 241591 > 4²³⁸ [i]