MinT - Best Known (107, 107+39, s)-Nets in Base 3

Best Known (107, 107+39, s)-Nets in Base 3

(107, 107+39, 264)-Net over F₃ — Constructive and digital

Digital (107, 146, 264)-net over F₃, using

1 times m-reduction [i] based on digital (107, 147, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 49, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(107, 107+39, 512)-Net over F₃ — Digital

Digital (107, 146, 512)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+39, 17334)-Net in Base 3 — Upper bound on s

There is no (107, 146, 17335)-net in base 3, because

1 times m-reduction [i] would yield (107, 145, 17335)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1523 441899 765395 280416 563522 465963 937562 255316 175342 717743 989864 861371 > 3¹⁴⁵ [i]