MinT - Best Known (161−63, 161, s)-Nets in Base 3

Best Known (161−63, 161, s)-Nets in Base 3

(161−63, 161, 148)-Net over F₃ — Constructive and digital

Digital (98, 161, 148)-net over F₃, using

1 times m-reduction [i] based on digital (98, 162, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 81, 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]

(161−63, 161, 166)-Net over F₃ — Digital

Digital (98, 161, 166)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−63, 161, 1770)-Net in Base 3 — Upper bound on s

There is no (98, 161, 1771)-net in base 3, because

1 times m-reduction [i] would yield (98, 160, 1771)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21876 239590 359892 465485 863404 455526 031621 643291 481703 091193 054780 217098 417779 > 3¹⁶⁰ [i]