MinT - Best Known (210−91, 210, s)-Nets in Base 3

Best Known (210−91, 210, s)-Nets in Base 3

(210−91, 210, 128)-Net over F₃ — Constructive and digital

Digital (119, 210, 128)-net over F₃, using

2 times m-reduction [i] based on digital (119, 212, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 106, 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]

(210−91, 210, 156)-Net over F₃ — Digital

Digital (119, 210, 156)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−91, 210, 1405)-Net in Base 3 — Upper bound on s

There is no (119, 210, 1406)-net in base 3, because

1 times m-reduction [i] would yield (119, 209, 1406)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5361 466483 242738 432451 503484 405717 015412 345423 312762 874769 097176 385325 213663 111157 681070 888530 671045 > 3²⁰⁹ [i]