MinT - Best Known (116, 116+90, s)-Nets in Base 3

Best Known (116, 116+90, s)-Nets in Base 3

(116, 116+90, 128)-Net over F₃ — Constructive and digital

Digital (116, 206, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 103, 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]

(116, 116+90, 150)-Net over F₃ — Digital

Digital (116, 206, 150)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+90, 1302)-Net in Base 3 — Upper bound on s

There is no (116, 206, 1303)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 194 353473 810277 162220 269653 169969 088953 604051 919229 525161 825318 048177 235211 567465 867336 000406 611607 > 3²⁰⁶ [i]