MinT - Best Known (151−59, 151, s)-Nets in Base 3

Best Known (151−59, 151, s)-Nets in Base 3

(151−59, 151, 128)-Net over F₃ — Constructive and digital

Digital (92, 151, 128)-net over F₃, using

7 times m-reduction [i] based on digital (92, 158, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 79, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(151−59, 151, 157)-Net over F₃ — Digital

Digital (92, 151, 157)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151−59, 151, 1685)-Net in Base 3 — Upper bound on s

There is no (92, 151, 1686)-net in base 3, because

1 times m-reduction [i] would yield (92, 150, 1686)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 373144 351029 650046 304742 123911 799253 529664 663189 028180 531562 476672 621397 > 3¹⁵⁰ [i]