MinT - Best Known (208−89, 208, s)-Nets in Base 3

Best Known (208−89, 208, s)-Nets in Base 3

(208−89, 208, 128)-Net over F₃ — Constructive and digital

Digital (119, 208, 128)-net over F₃, using

4 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]

(208−89, 208, 160)-Net over F₃ — Digital

Digital (119, 208, 160)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−89, 208, 1472)-Net in Base 3 — Upper bound on s

There is no (119, 208, 1473)-net in base 3, because

1 times m-reduction [i] would yield (119, 207, 1473)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 590 641721 745367 665085 723971 851510 714468 956396 255506 229840 065964 325306 183089 939863 629038 993437 350001 > 3²⁰⁷ [i]