MinT - Best Known (162, 232, s)-Nets in Base 4

Best Known (162, 232, s)-Nets in Base 4

(162, 232, 531)-Net over F₄ — Constructive and digital

Digital (162, 232, 531)-net over F₄, using

4¹ times duplication [i] based on digital (161, 231, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 77, 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]

(162, 232, 920)-Net over F₄ — Digital

Digital (162, 232, 920)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 232, 45359)-Net in Base 4 — Upper bound on s

There is no (162, 232, 45360)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 661622 210471 775628 637391 184662 129873 611947 789089 698538 624000 132179 003216 217017 481641 982489 923228 752604 252540 346787 211082 827628 812645 028965 > 4²³² [i]