MinT - Best Known (207−63, 207, s)-Nets in Base 3

Best Known (207−63, 207, s)-Nets in Base 3

(207−63, 207, 228)-Net over F₃ — Constructive and digital

Digital (144, 207, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 69, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(207−63, 207, 436)-Net over F₃ — Digital

Digital (144, 207, 436)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−63, 207, 9164)-Net in Base 3 — Upper bound on s

There is no (144, 207, 9165)-net in base 3, because

1 times m-reduction [i] would yield (144, 206, 9165)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 946580 494018 214140 961678 178819 116700 444621 103918 484689 127771 936821 903506 225379 184682 299261 678555 > 3²⁰⁶ [i]