MinT - Best Known (164, 241, s)-Nets in Base 4

Best Known (164, 241, s)-Nets in Base 4

(164, 241, 450)-Net over F₄ — Constructive and digital

Digital (164, 241, 450)-net over F₄, using

7 times m-reduction [i] based on digital (164, 248, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 124, 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]

(164, 241, 759)-Net over F₄ — Digital

Digital (164, 241, 759)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 241, 31749)-Net in Base 4 — Upper bound on s

There is no (164, 241, 31750)-net in base 4, because

1 times m-reduction [i] would yield (164, 240, 31750)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 122733 248242 182567 800737 073404 095859 074837 239270 419464 103276 894612 699758 726254 398064 893003 115070 345472 415343 250667 849292 329782 401610 249522 299136 > 4²⁴⁰ [i]