MinT - Best Known (244−67, 244, s)-Nets in Base 4

Best Known (244−67, 244, s)-Nets in Base 4

(244−67, 244, 531)-Net over F₄ — Constructive and digital

Digital (177, 244, 531)-net over F₄, using

11 times m-reduction [i] based on digital (177, 255, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 85, 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]

(244−67, 244, 1439)-Net over F₄ — Digital

Digital (177, 244, 1439)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−67, 244, 118983)-Net in Base 4 — Upper bound on s

There is no (177, 244, 118984)-net in base 4, because

1 times m-reduction [i] would yield (177, 243, 118984)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 199 843432 667492 748964 043175 012552 531227 327938 343778 596434 332502 079972 495934 035399 657708 901088 915758 906164 181582 394634 234116 626697 337048 238413 298754 > 4²⁴³ [i]