MinT - Best Known (193−57, 193, s)-Nets in Base 4

Best Known (193−57, 193, s)-Nets in Base 4

(193−57, 193, 531)-Net over F₄ — Constructive and digital

Digital (136, 193, 531)-net over F₄, using

4¹ times duplication [i] based on digital (135, 192, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 64, 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]

(193−57, 193, 860)-Net over F₄ — Digital

Digital (136, 193, 860)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−57, 193, 50594)-Net in Base 4 — Upper bound on s

There is no (136, 193, 50595)-net in base 4, because

1 times m-reduction [i] would yield (136, 192, 50595)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 39 423284 113319 733457 596079 253623 819759 286319 411309 660943 423354 150193 023363 975532 770864 556840 002595 473271 866394 828968 > 4¹⁹² [i]