MinT - Best Known (155−59, 155, s)-Nets in Base 3

Best Known (155−59, 155, s)-Nets in Base 3

(155−59, 155, 148)-Net over F₃ — Constructive and digital

Digital (96, 155, 148)-net over F₃, using

3 times m-reduction [i] based on digital (96, 158, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 79, 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]

(155−59, 155, 173)-Net over F₃ — Digital

Digital (96, 155, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(155−59, 155, 1965)-Net in Base 3 — Upper bound on s

There is no (96, 155, 1966)-net in base 3, because

1 times m-reduction [i] would yield (96, 154, 1966)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30 022842 977933 998670 383832 389644 002048 728441 590338 886485 722893 287146 312389 > 3¹⁵⁴ [i]