MinT - Best Known (117, 165, s)-Nets in Base 4

Best Known (117, 165, s)-Nets in Base 4

(117, 165, 531)-Net over F₄ — Constructive and digital

Digital (117, 165, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 55, 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]

(117, 165, 808)-Net over F₄ — Digital

Digital (117, 165, 808)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 165, 45000)-Net in Base 4 — Upper bound on s

There is no (117, 165, 45001)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2188 019685 368089 001824 675170 958309 378342 838017 323818 851392 469360 109612 793445 243651 932773 199835 612156 > 4¹⁶⁵ [i]