MinT - Best Known (249−70, 249, s)-Nets in Base 4

Best Known (249−70, 249, s)-Nets in Base 4

(249−70, 249, 531)-Net over F₄ — Constructive and digital

Digital (179, 249, 531)-net over F₄, using

9 times m-reduction [i] based on digital (179, 258, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 86, 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]

(249−70, 249, 1319)-Net over F₄ — Digital

Digital (179, 249, 1319)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−70, 249, 88967)-Net in Base 4 — Upper bound on s

There is no (179, 249, 88968)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 818637 403379 571716 478570 170025 155469 818059 194432 164585 243725 930236 229091 356199 788442 920448 307607 993932 710920 714883 995373 669054 960225 073666 773804 396500 > 4²⁴⁹ [i]