MinT - Best Known (169, 169+69, s)-Nets in Base 3

Best Known (169, 169+69, s)-Nets in Base 3

(169, 169+69, 282)-Net over F₃ — Constructive and digital

Digital (169, 238, 282)-net over F₃, using

3¹ times duplication [i] based on digital (168, 237, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 79, 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]

(169, 169+69, 576)-Net over F₃ — Digital

Digital (169, 238, 576)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 169+69, 14297)-Net in Base 3 — Upper bound on s

There is no (169, 238, 14298)-net in base 3, because

1 times m-reduction [i] would yield (169, 237, 14298)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119877 483490 340395 891880 378971 220668 995110 999796 331425 192588 597062 881620 237029 329631 981965 072458 707767 269511 115685 > 3²³⁷ [i]