MinT - Best Known (161−72, 161, s)-Nets in Base 3

Best Known (161−72, 161, s)-Nets in Base 3

(161−72, 161, 80)-Net over F₃ — Constructive and digital

Digital (89, 161, 80)-net over F₃, using

1 times m-reduction [i] based on digital (89, 162, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 81, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(161−72, 161, 114)-Net over F₃ — Digital

Digital (89, 161, 114)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−72, 161, 936)-Net in Base 3 — Upper bound on s

There is no (89, 161, 937)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 66379 888501 506013 361065 641528 065025 217185 923594 567863 674923 029772 001196 614545 > 3¹⁶¹ [i]