MinT - Best Known (221−97, 221, s)-Nets in Base 3

Best Known (221−97, 221, s)-Nets in Base 3

(221−97, 221, 128)-Net over F₃ — Constructive and digital

Digital (124, 221, 128)-net over F₃, using

1 times m-reduction [i] based on digital (124, 222, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 111, 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]

(221−97, 221, 157)-Net over F₃ — Digital

Digital (124, 221, 157)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−97, 221, 1393)-Net in Base 3 — Upper bound on s

There is no (124, 221, 1394)-net in base 3, because

1 times m-reduction [i] would yield (124, 220, 1394)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 931 864740 583683 418149 234222 430163 229051 138452 459447 078792 570976 840944 875907 184509 041370 593561 016823 740385 > 3²²⁰ [i]