MinT - Best Known (211−58, 211, s)-Nets in Base 4

Best Known (211−58, 211, s)-Nets in Base 4

(211−58, 211, 531)-Net over F₄ — Constructive and digital

Digital (153, 211, 531)-net over F₄, using

8 times m-reduction [i] based on digital (153, 219, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 73, 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]

(211−58, 211, 1268)-Net over F₄ — Digital

Digital (153, 211, 1268)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−58, 211, 93410)-Net in Base 4 — Upper bound on s

There is no (153, 211, 93411)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 832044 418047 342210 502921 606586 147201 277607 049377 651652 653040 723653 933818 199499 062502 069260 837974 672085 676302 749408 032792 294352 > 4²¹¹ [i]