MinT - Best Known (117, 117+45, s)-Nets in Base 4

Best Known (117, 117+45, s)-Nets in Base 4

(117, 117+45, 531)-Net over F₄ — Constructive and digital

Digital (117, 162, 531)-net over F₄, using

3 times m-reduction [i] based on 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, 117+45, 969)-Net over F₄ — Digital

Digital (117, 162, 969)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+45, 76844)-Net in Base 4 — Upper bound on s

There is no (117, 162, 76845)-net in base 4, because

1 times m-reduction [i] would yield (117, 161, 76845)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 544002 785647 154363 425618 940246 934359 028147 713570 956291 693413 666657 323850 310748 699917 687982 160104 > 4¹⁶¹ [i]