MinT - Best Known (123, 123+85, s)-Nets in Base 3

Best Known (123, 123+85, s)-Nets in Base 3

(123, 123+85, 148)-Net over F₃ — Constructive and digital

Digital (123, 208, 148)-net over F₃, using

4 times m-reduction [i] based on digital (123, 212, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 106, 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]

(123, 123+85, 182)-Net over F₃ — Digital

Digital (123, 208, 182)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+85, 1813)-Net in Base 3 — Upper bound on s

There is no (123, 208, 1814)-net in base 3, because

1 times m-reduction [i] would yield (123, 207, 1814)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 585 030433 002816 957207 042435 580061 292946 382850 690633 842673 620883 810952 663522 035489 374665 957769 885469 > 3²⁰⁷ [i]