MinT - Best Known (226−105, 226, s)-Nets in Base 3

Best Known (226−105, 226, s)-Nets in Base 3

(226−105, 226, 80)-Net over F₃ — Constructive and digital

Digital (121, 226, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 113, 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]

(226−105, 226, 137)-Net over F₃ — Digital

Digital (121, 226, 137)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−105, 226, 1122)-Net in Base 3 — Upper bound on s

There is no (121, 226, 1123)-net in base 3, because

1 times m-reduction [i] would yield (121, 225, 1123)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 229914 249958 924585 537370 397848 400345 206164 983245 549791 409277 269026 705023 969891 107430 466105 727173 346571 362937 > 3²²⁵ [i]