MinT - Best Known (167, 167+63, s)-Nets in Base 4

Best Known (167, 167+63, s)-Nets in Base 4

(167, 167+63, 531)-Net over F₄ — Constructive and digital

Digital (167, 230, 531)-net over F₄, using

10 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]

(167, 167+63, 1385)-Net over F₄ — Digital

Digital (167, 230, 1385)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+63, 115955)-Net in Base 4 — Upper bound on s

There is no (167, 230, 115956)-net in base 4, because

1 times m-reduction [i] would yield (167, 229, 115956)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 744334 059221 328591 254506 395390 643662 551706 701366 974067 286722 531785 240078 628978 064530 421158 592919 349802 417656 275969 915921 932318 634719 753784 > 4²²⁹ [i]