MinT - Best Known (172, 172+82, s)-Nets in Base 4

Best Known (172, 172+82, s)-Nets in Base 4

(172, 172+82, 450)-Net over F₄ — Constructive and digital

Digital (172, 254, 450)-net over F₄, using

t-expansion [i] based on digital (170, 254, 450)-net over F₄, using
- 6 times m-reduction [i] based on digital (170, 260, 450)-net over F₄, using
  - trace code for nets [i] based on digital (40, 130, 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]

(172, 172+82, 764)-Net over F₄ — Digital

Digital (172, 254, 764)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+82, 28848)-Net in Base 4 — Upper bound on s

There is no (172, 254, 28849)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 838 807033 957285 346597 577954 557513 900070 991085 584533 085630 832169 840553 845509 036390 391937 455539 829403 756529 848162 659230 845732 692302 571856 403457 512988 015064 > 4²⁵⁴ [i]