MinT - Best Known (119, 164, s)-Nets in Base 4

Best Known (119, 164, s)-Nets in Base 4

(119, 164, 531)-Net over F₄ — Constructive and digital

Digital (119, 164, 531)-net over F₄, using

4 times m-reduction [i] based on digital (119, 168, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 56, 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]

(119, 164, 1031)-Net over F₄ — Digital

Digital (119, 164, 1031)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 164, 87168)-Net in Base 4 — Upper bound on s

There is no (119, 164, 87169)-net in base 4, because

1 times m-reduction [i] would yield (119, 163, 87169)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 136 716442 422922 088112 893030 943866 370355 538229 266081 824710 928872 279273 064379 300267 978235 915010 957120 > 4¹⁶³ [i]