MinT - Best Known (153, 153+68, s)-Nets in Base 4

Best Known (153, 153+68, s)-Nets in Base 4

(153, 153+68, 450)-Net over F₄ — Constructive and digital

Digital (153, 221, 450)-net over F₄, using

5 times m-reduction [i] based on digital (153, 226, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 113, 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]

(153, 153+68, 815)-Net over F₄ — Digital

Digital (153, 221, 815)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(153, 153+68, 36933)-Net in Base 4 — Upper bound on s

There is no (153, 221, 36934)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 365119 127938 120932 165687 582038 547266 923586 778717 771315 413204 943571 010566 200510 357415 315774 017036 710158 867318 233390 312299 664399 041420 > 4²²¹ [i]