MinT - Best Known (136−35, 136, s)-Nets in Base 3

Best Known (136−35, 136, s)-Nets in Base 3

(136−35, 136, 282)-Net over F₃ — Constructive and digital

Digital (101, 136, 282)-net over F₃, using

3¹ times duplication [i] based on digital (100, 135, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 45, 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]

(136−35, 136, 561)-Net over F₃ — Digital

Digital (101, 136, 561)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−35, 136, 22054)-Net in Base 3 — Upper bound on s

There is no (101, 136, 22055)-net in base 3, because

1 times m-reduction [i] would yield (101, 135, 22055)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25797 707895 637882 563015 822138 081913 288547 715508 071201 544775 825967 > 3¹³⁵ [i]