MinT - Best Known (234−65, 234, s)-Nets in Base 4

Best Known (234−65, 234, s)-Nets in Base 4

(234−65, 234, 531)-Net over F₄ — Constructive and digital

Digital (169, 234, 531)-net over F₄, using

9 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]

(234−65, 234, 1319)-Net over F₄ — Digital

Digital (169, 234, 1319)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−65, 234, 103133)-Net in Base 4 — Upper bound on s

There is no (169, 234, 103134)-net in base 4, because

1 times m-reduction [i] would yield (169, 233, 103134)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 586960 617453 458782 952665 027164 923504 276212 674799 809017 312717 454464 467078 676460 640451 052835 823812 740900 441779 226810 332221 509028 458144 540990 > 4²³³ [i]