MinT - Best Known (246−73, 246, s)-Nets in Base 3

Best Known (246−73, 246, s)-Nets in Base 3

(246−73, 246, 264)-Net over F₃ — Constructive and digital

Digital (173, 246, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 82, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(246−73, 246, 550)-Net over F₃ — Digital

Digital (173, 246, 550)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−73, 246, 12576)-Net in Base 3 — Upper bound on s

There is no (173, 246, 12577)-net in base 3, because

1 times m-reduction [i] would yield (173, 245, 12577)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 785 842455 290382 903766 344879 389585 123215 520547 417418 499694 034950 754970 138945 188909 853909 282903 315459 723911 919495 247825 > 3²⁴⁵ [i]