MinT - Best Known (109, 109+45, s)-Nets in Base 3

Best Known (109, 109+45, s)-Nets in Base 3

(109, 109+45, 228)-Net over F₃ — Constructive and digital

Digital (109, 154, 228)-net over F₃, using

3¹ times duplication [i] based on digital (108, 153, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 51, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(109, 109+45, 387)-Net over F₃ — Digital

Digital (109, 154, 387)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+45, 9397)-Net in Base 3 — Upper bound on s

There is no (109, 154, 9398)-net in base 3, because

1 times m-reduction [i] would yield (109, 153, 9398)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 011178 964902 241173 702860 113585 939358 517434 727135 605648 548142 461726 589717 > 3¹⁵³ [i]