MinT - Best Known (177−77, 177, s)-Nets in Base 3

Best Known (177−77, 177, s)-Nets in Base 3

(177−77, 177, 80)-Net over F₃ — Constructive and digital

Digital (100, 177, 80)-net over F₃, using

7 times m-reduction [i] based on digital (100, 184, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 92, 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]

(177−77, 177, 133)-Net over F₃ — Digital

Digital (100, 177, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−77, 177, 1180)-Net in Base 3 — Upper bound on s

There is no (100, 177, 1181)-net in base 3, because

1 times m-reduction [i] would yield (100, 176, 1181)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 945299 026542 840064 774832 227906 835771 381877 527292 981830 554990 286203 725710 838873 580209 > 3¹⁷⁶ [i]