MinT - Best Known (229−73, 229, s)-Nets in Base 4

Best Known (229−73, 229, s)-Nets in Base 4

(229−73, 229, 450)-Net over F₄ — Constructive and digital

Digital (156, 229, 450)-net over F₄, using

3 times m-reduction [i] based on digital (156, 232, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 116, 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]

(229−73, 229, 732)-Net over F₄ — Digital

Digital (156, 229, 732)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−73, 229, 30920)-Net in Base 4 — Upper bound on s

There is no (156, 229, 30921)-net in base 4, because

1 times m-reduction [i] would yield (156, 228, 30921)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186148 983979 096560 227196 017910 788766 342276 009572 375740 879049 342265 032728 998112 427215 339707 555961 440338 660925 787339 229269 301135 428470 638188 > 4²²⁸ [i]