MinT - Best Known (115, 158, s)-Nets in Base 4

Best Known (115, 158, s)-Nets in Base 4

(115, 158, 531)-Net over F₄ — Constructive and digital

Digital (115, 158, 531)-net over F₄, using

4 times m-reduction [i] based on digital (115, 162, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 54, 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]

(115, 158, 1034)-Net over F₄ — Digital

Digital (115, 158, 1034)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 158, 91707)-Net in Base 4 — Upper bound on s

There is no (115, 158, 91708)-net in base 4, because

1 times m-reduction [i] would yield (115, 157, 91708)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 33376 780716 798916 344618 654948 377968 263823 663741 538326 890756 656556 475673 640579 454637 096384 503810 > 4¹⁵⁷ [i]