MinT - Best Known (170, 239, s)-Nets in Base 4

Best Known (170, 239, s)-Nets in Base 4

(170, 239, 531)-Net over F₄ — Constructive and digital

Digital (170, 239, 531)-net over F₄, using

t-expansion [i] based on digital (169, 239, 531)-net over F₄, using
- 4 times m-reduction [i] based on digital (169, 243, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 81, 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]

(170, 239, 1134)-Net over F₄ — Digital

Digital (170, 239, 1134)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(170, 239, 73894)-Net in Base 4 — Upper bound on s

There is no (170, 239, 73895)-net in base 4, because

1 times m-reduction [i] would yield (170, 238, 73895)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 195177 521366 156447 335456 297915 983080 582141 365136 714352 356046 723925 589817 341475 346743 688517 747335 849641 540813 142182 032870 649051 254797 972906 456387 > 4²³⁸ [i]