MinT - Best Known (123, 123+47, s)-Nets in Base 4

Best Known (123, 123+47, s)-Nets in Base 4

(123, 123+47, 531)-Net over F₄ — Constructive and digital

Digital (123, 170, 531)-net over F₄, using

4 times m-reduction [i] based on digital (123, 174, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 58, 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]

(123, 123+47, 1030)-Net over F₄ — Digital

Digital (123, 170, 1030)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+47, 83381)-Net in Base 4 — Upper bound on s

There is no (123, 170, 83382)-net in base 4, because

1 times m-reduction [i] would yield (123, 169, 83382)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 560006 731863 878983 086258 190134 042971 806761 683374 185210 604066 292540 342735 349222 907990 357465 069699 845952 > 4¹⁶⁹ [i]