MinT - Best Known (166, 166+75, s)-Nets in Base 4

Best Known (166, 166+75, s)-Nets in Base 4

(166, 166+75, 450)-Net over F₄ — Constructive and digital

Digital (166, 241, 450)-net over F₄, using

11 times m-reduction [i] based on digital (166, 252, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 126, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(166, 166+75, 840)-Net over F₄ — Digital

Digital (166, 241, 840)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(166, 166+75, 39238)-Net in Base 4 — Upper bound on s

There is no (166, 241, 39239)-net in base 4, because

1 times m-reduction [i] would yield (166, 240, 39239)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 124110 783352 597026 586735 851100 980097 781803 846018 560534 764746 983735 026058 499054 006695 840140 935667 588934 160189 946137 345987 422255 595168 667555 162020 > 4²⁴⁰ [i]