MinT - Best Known (160, 160+80, s)-Nets in Base 4

Best Known (160, 160+80, s)-Nets in Base 4

(160, 160+80, 450)-Net over F₄ — Constructive and digital

Digital (160, 240, 450)-net over F₄, using

trace code for nets [i] based on digital (40, 120, 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]

(160, 160+80, 646)-Net over F₄ — Digital

Digital (160, 240, 646)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(160, 160+80, 21496)-Net in Base 4 — Upper bound on s

There is no (160, 240, 21497)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 124757 791042 202370 065865 756796 866732 818584 024161 026165 372044 599147 194412 048578 997898 142233 830935 407993 067164 336707 870828 606419 981710 139969 046571 > 4²⁴⁰ [i]