MinT - Best Known (246−78, 246, s)-Nets in Base 3

Best Known (246−78, 246, s)-Nets in Base 3

(246−78, 246, 192)-Net over F₃ — Constructive and digital

Digital (168, 246, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 82, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(246−78, 246, 446)-Net over F₃ — Digital

Digital (168, 246, 446)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−78, 246, 7830)-Net in Base 3 — Upper bound on s

There is no (168, 246, 7831)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2356 971635 813058 622986 451893 138937 912160 909138 674449 107119 579816 876005 281383 507935 448973 673889 710685 387514 677830 750099 > 3²⁴⁶ [i]