MinT - Best Known (163, 163+83, s)-Nets in Base 4

Best Known (163, 163+83, s)-Nets in Base 4

(163, 163+83, 450)-Net over F₄ — Constructive and digital

Digital (163, 246, 450)-net over F₄, using

trace code for nets [i] based on digital (40, 123, 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]

(163, 163+83, 632)-Net over F₄ — Digital

Digital (163, 246, 632)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+83, 21270)-Net in Base 4 — Upper bound on s

There is no (163, 246, 21271)-net in base 4, because

1 times m-reduction [i] would yield (163, 245, 21271)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3198 821289 487417 297244 867768 239003 918018 139564 744994 934603 832902 973028 272843 712684 313573 954648 761249 124319 068034 776774 160932 902777 504823 992889 571296 > 4²⁴⁵ [i]