MinT - Best Known (234−73, 234, s)-Nets in Base 4

Best Known (234−73, 234, s)-Nets in Base 4

(234−73, 234, 450)-Net over F₄ — Constructive and digital

Digital (161, 234, 450)-net over F₄, using

8 times m-reduction [i] based on digital (161, 242, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 121, 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]

(234−73, 234, 811)-Net over F₄ — Digital

Digital (161, 234, 811)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−73, 234, 37492)-Net in Base 4 — Upper bound on s

There is no (161, 234, 37493)-net in base 4, because

1 times m-reduction [i] would yield (161, 233, 37493)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 690869 833617 148128 527169 518047 766337 906925 637967 799040 881042 130432 139088 310962 790220 230342 480124 674324 881207 009772 464605 795661 873682 564805 > 4²³³ [i]