MinT - Best Known (128, 128+102, s)-Nets in Base 3

Best Known (128, 128+102, s)-Nets in Base 3

(128, 128+102, 128)-Net over F₃ — Constructive and digital

Digital (128, 230, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 115, 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]

(128, 128+102, 158)-Net over F₃ — Digital

Digital (128, 230, 158)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+102, 1358)-Net in Base 3 — Upper bound on s

There is no (128, 230, 1359)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56 567198 702630 359946 621774 142293 618481 027861 939833 109309 966004 151284 631923 660491 956029 199553 667492 428215 097819 > 3²³⁰ [i]