MinT - Best Known (184, 249, s)-Nets in Base 3

Best Known (184, 249, s)-Nets in Base 3

(184, 249, 324)-Net over F₃ — Constructive and digital

Digital (184, 249, 324)-net over F₃, using

trace code for nets [i] based on digital (18, 83, 108)-net over F₂₇, using
- net from sequence [i] based on digital (18, 107)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 18 and N(F) ≥ 108, using
    - F₃ from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F₂₇ [i]

(184, 249, 865)-Net over F₃ — Digital

Digital (184, 249, 865)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(184, 249, 31850)-Net in Base 3 — Upper bound on s

There is no (184, 249, 31851)-net in base 3, because

1 times m-reduction [i] would yield (184, 248, 31851)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21205 974562 360433 267013 774612 327914 099469 988039 913722 101245 075703 856902 852872 636055 500301 864359 330663 335784 365772 528577 > 3²⁴⁸ [i]