MinT - Best Known (172−50, 172, s)-Nets in Base 4

Best Known (172−50, 172, s)-Nets in Base 4

(172−50, 172, 531)-Net over F₄ — Constructive and digital

Digital (122, 172, 531)-net over F₄, using

4¹ times duplication [i] based on digital (121, 171, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 57, 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]

(172−50, 172, 837)-Net over F₄ — Digital

Digital (122, 172, 837)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−50, 172, 47042)-Net in Base 4 — Upper bound on s

There is no (122, 172, 47043)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 846932 328432 124166 872978 071906 915966 957975 685644 977819 199654 544017 159709 451063 126658 366845 637057 542192 > 4¹⁷² [i]