MinT - Best Known (144, 144+91, s)-Nets in Base 3

Best Known (144, 144+91, s)-Nets in Base 3

(144, 144+91, 156)-Net over F₃ — Constructive and digital

Digital (144, 235, 156)-net over F₃, using

9 times m-reduction [i] based on digital (144, 244, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 122, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(144, 144+91, 236)-Net over F₃ — Digital

Digital (144, 235, 236)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+91, 2623)-Net in Base 3 — Upper bound on s

There is no (144, 235, 2624)-net in base 3, because

1 times m-reduction [i] would yield (144, 234, 2624)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4449 530377 275334 526413 102017 664016 468882 039099 570229 503429 828677 151690 241257 986256 065210 259488 713748 315356 782721 > 3²³⁴ [i]