MinT - Best Known (171−46, 171, s)-Nets in Base 4

Best Known (171−46, 171, s)-Nets in Base 4

(171−46, 171, 531)-Net over F₄ — Constructive and digital

Digital (125, 171, 531)-net over F₄, using

6 times m-reduction [i] based on digital (125, 177, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 59, 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]

(171−46, 171, 1162)-Net over F₄ — Digital

Digital (125, 171, 1162)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−46, 171, 94066)-Net in Base 4 — Upper bound on s

There is no (125, 171, 94067)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 960536 416046 693451 614169 950687 072801 447684 780317 458262 980310 428919 085220 292559 176740 724686 652748 078912 > 4¹⁷¹ [i]