MinT - Best Known (234−67, 234, s)-Nets in Base 4

Best Known (234−67, 234, s)-Nets in Base 4

(234−67, 234, 531)-Net over F₄ — Constructive and digital

Digital (167, 234, 531)-net over F₄, using

6 times m-reduction [i] based on digital (167, 240, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 80, 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]

(234−67, 234, 1154)-Net over F₄ — Digital

Digital (167, 234, 1154)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−67, 234, 78161)-Net in Base 4 — Upper bound on s

There is no (167, 234, 78162)-net in base 4, because

1 times m-reduction [i] would yield (167, 233, 78162)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 599519 364669 230399 124703 497172 230949 106544 594515 567119 824288 406521 640175 731327 587326 286238 101574 787260 988045 562362 181519 250287 363638 055030 > 4²³³ [i]