MinT - Best Known (237−73, 237, s)-Nets in Base 3

Best Known (237−73, 237, s)-Nets in Base 3

(237−73, 237, 228)-Net over F₃ — Constructive and digital

Digital (164, 237, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 79, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(237−73, 237, 473)-Net over F₃ — Digital

Digital (164, 237, 473)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−73, 237, 9547)-Net in Base 3 — Upper bound on s

There is no (164, 237, 9548)-net in base 3, because

1 times m-reduction [i] would yield (164, 236, 9548)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 39932 321851 160374 701229 025625 061863 300952 005749 550623 240655 968141 653897 993267 690304 309795 189095 692110 837718 039425 > 3²³⁶ [i]