MinT - Best Known (113, 113+43, s)-Nets in Base 4

Best Known (113, 113+43, s)-Nets in Base 4

(113, 113+43, 531)-Net over F₄ — Constructive and digital

Digital (113, 156, 531)-net over F₄, using

3 times m-reduction [i] based on digital (113, 159, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 53, 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]

(113, 113+43, 969)-Net over F₄ — Digital

Digital (113, 156, 969)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+43, 80362)-Net in Base 4 — Upper bound on s

There is no (113, 156, 80363)-net in base 4, because

1 times m-reduction [i] would yield (113, 155, 80363)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2085 980858 295538 857088 505036 840133 891964 502892 344809 931219 495266 705913 102599 596377 653424 182840 > 4¹⁵⁵ [i]