MinT - Best Known (169, 169+42, s)-Nets in Base 4

Best Known (169, 169+42, s)-Nets in Base 4

(169, 169+42, 1539)-Net over F₄ — Constructive and digital

Digital (169, 211, 1539)-net over F₄, using

4¹ times duplication [i] based on digital (168, 210, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 70, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(169, 169+42, 6769)-Net over F₄ — Digital

Digital (169, 211, 6769)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 169+42, 3240697)-Net in Base 4 — Upper bound on s

There is no (169, 211, 3240698)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 830788 194913 639389 430403 766142 550751 848192 825032 203952 984681 415847 105033 685164 039353 722837 407260 266544 678116 926992 682932 500890 > 4²¹¹ [i]