MinT - Best Known (166, 166+79, s)-Nets in Base 4

Best Known (166, 166+79, s)-Nets in Base 4

(166, 166+79, 450)-Net over F₄ — Constructive and digital

Digital (166, 245, 450)-net over F₄, using

7 times m-reduction [i] based on digital (166, 252, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 126, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(166, 166+79, 744)-Net over F₄ — Digital

Digital (166, 245, 744)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(166, 166+79, 29962)-Net in Base 4 — Upper bound on s

There is no (166, 245, 29963)-net in base 4, because

1 times m-reduction [i] would yield (166, 244, 29963)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 799 912077 260835 382547 383666 291778 613805 732371 908991 651499 914318 036534 180463 509548 425909 943541 651850 910385 563527 990176 002721 722651 162120 366610 613504 > 4²⁴⁴ [i]