MinT - Best Known (161−59, 161, s)-Nets in Base 3

Best Known (161−59, 161, s)-Nets in Base 3

(161−59, 161, 148)-Net over F₃ — Constructive and digital

Digital (102, 161, 148)-net over F₃, using

9 times m-reduction [i] based on digital (102, 170, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 85, 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]

(161−59, 161, 199)-Net over F₃ — Digital

Digital (102, 161, 199)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−59, 161, 2474)-Net in Base 3 — Upper bound on s

There is no (102, 161, 2475)-net in base 3, because

1 times m-reduction [i] would yield (102, 160, 2475)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21904 502993 265507 563498 536857 950933 122425 266178 131972 948302 316211 585300 575519 > 3¹⁶⁰ [i]