MinT - Best Known (158−59, 158, s)-Nets in Base 3

Best Known (158−59, 158, s)-Nets in Base 3

(158−59, 158, 148)-Net over F₃ — Constructive and digital

Digital (99, 158, 148)-net over F₃, using

6 times m-reduction [i] based on digital (99, 164, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 82, 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]

(158−59, 158, 186)-Net over F₃ — Digital

Digital (99, 158, 186)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−59, 158, 2205)-Net in Base 3 — Upper bound on s

There is no (99, 158, 2206)-net in base 3, because

1 times m-reduction [i] would yield (99, 157, 2206)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 810 421812 215212 856694 356215 107353 808175 278384 018121 778406 836953 649885 284389 > 3¹⁵⁷ [i]