MinT - Best Known (138, 138+112, s)-Nets in Base 3

Best Known (138, 138+112, s)-Nets in Base 3

(138, 138+112, 128)-Net over F₃ — Constructive and digital

Digital (138, 250, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 125, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(138, 138+112, 166)-Net over F₃ — Digital

Digital (138, 250, 166)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+112, 1409)-Net in Base 3 — Upper bound on s

There is no (138, 250, 1410)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193533 409520 916849 741592 536657 922546 283614 507104 734521 134963 274260 002830 238232 303462 197607 434026 162026 379210 723488 843825 > 3²⁵⁰ [i]