MinT - Best Known (221−101, 221, s)-Nets in Base 3

Best Known (221−101, 221, s)-Nets in Base 3

(221−101, 221, 80)-Net over F₃ — Constructive and digital

Digital (120, 221, 80)-net over F₃, using

3 times m-reduction [i] based on digital (120, 224, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 112, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(221−101, 221, 141)-Net over F₃ — Digital

Digital (120, 221, 141)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−101, 221, 1175)-Net in Base 3 — Upper bound on s

There is no (120, 221, 1176)-net in base 3, because

1 times m-reduction [i] would yield (120, 220, 1176)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 932 439414 090467 646847 730356 852319 419695 298374 154330 113785 081723 955427 630653 960406 647945 241024 074914 725137 > 3²²⁰ [i]