MinT - Best Known (151−55, 151, s)-Nets in Base 3

Best Known (151−55, 151, s)-Nets in Base 3

(151−55, 151, 148)-Net over F₃ — Constructive and digital

Digital (96, 151, 148)-net over F₃, using

7 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]

(151−55, 151, 192)-Net over F₃ — Digital

Digital (96, 151, 192)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151−55, 151, 2417)-Net in Base 3 — Upper bound on s

There is no (96, 151, 2418)-net in base 3, because

1 times m-reduction [i] would yield (96, 150, 2418)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 372722 454216 814784 452573 690061 427878 844953 938912 983962 721628 209461 327905 > 3¹⁵⁰ [i]