MinT - Best Known (143−37, 143, s)-Nets in Base 3

Best Known (143−37, 143, s)-Nets in Base 3

(143−37, 143, 282)-Net over F₃ — Constructive and digital

Digital (106, 143, 282)-net over F₃, using

1 times m-reduction [i] based on digital (106, 144, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 48, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(143−37, 143, 570)-Net over F₃ — Digital

Digital (106, 143, 570)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−37, 143, 21913)-Net in Base 3 — Upper bound on s

There is no (106, 143, 21914)-net in base 3, because

1 times m-reduction [i] would yield (106, 142, 21914)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56 419193 002366 793360 231687 566611 772076 485236 893005 426725 817214 204805 > 3¹⁴² [i]