MinT - Best Known (109−33, 109, s)-Nets in Base 3

Best Known (109−33, 109, s)-Nets in Base 3

(109−33, 109, 156)-Net over F₃ — Constructive and digital

Digital (76, 109, 156)-net over F₃, using

3¹ times duplication [i] based on digital (75, 108, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 36, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(109−33, 109, 262)-Net over F₃ — Digital

Digital (76, 109, 262)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−33, 109, 5634)-Net in Base 3 — Upper bound on s

There is no (76, 109, 5635)-net in base 3, because

1 times m-reduction [i] would yield (76, 108, 5635)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3382 427819 150786 333322 634213 225068 663725 942496 408801 > 3¹⁰⁸ [i]