MinT - Best Known (241−78, 241, s)-Nets in Base 4

Best Known (241−78, 241, s)-Nets in Base 4

(241−78, 241, 450)-Net over F₄ — Constructive and digital

Digital (163, 241, 450)-net over F₄, using

5 times m-reduction [i] based on digital (163, 246, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 123, 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]

(241−78, 241, 723)-Net over F₄ — Digital

Digital (163, 241, 723)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−78, 241, 26928)-Net in Base 4 — Upper bound on s

There is no (163, 241, 26929)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 497943 974824 540717 956138 063758 588398 264510 484379 733000 344048 216440 913759 195782 030045 071780 153044 613183 500166 199992 134612 862582 155507 209021 403280 > 4²⁴¹ [i]