MinT - Best Known (109, 109+67, s)-Nets in Base 3

Best Known (109, 109+67, s)-Nets in Base 3

(109, 109+67, 148)-Net over F₃ — Constructive and digital

Digital (109, 176, 148)-net over F₃, using

8 times m-reduction [i] based on digital (109, 184, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 92, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(109, 109+67, 193)-Net over F₃ — Digital

Digital (109, 176, 193)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+67, 2198)-Net in Base 3 — Upper bound on s

There is no (109, 176, 2199)-net in base 3, because

1 times m-reduction [i] would yield (109, 175, 2199)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 314587 617261 143229 971940 139325 728717 165784 463381 057033 270376 284506 881573 080702 739695 > 3¹⁷⁵ [i]