MinT - Best Known (117, 117+91, s)-Nets in Base 3

Best Known (117, 117+91, s)-Nets in Base 3

(117, 117+91, 128)-Net over F₃ — Constructive and digital

Digital (117, 208, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 104, 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]

(117, 117+91, 150)-Net over F₃ — Digital

Digital (117, 208, 150)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+91, 1336)-Net in Base 3 — Upper bound on s

There is no (117, 208, 1337)-net in base 3, because

1 times m-reduction [i] would yield (117, 207, 1337)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 597 047593 158546 526535 164232 218008 412138 632982 895181 875503 165128 258152 907956 098569 327724 230499 770051 > 3²⁰⁷ [i]