MinT - Best Known (146−51, 146, s)-Nets in Base 3

Best Known (146−51, 146, s)-Nets in Base 3

(146−51, 146, 156)-Net over F₃ — Constructive and digital

Digital (95, 146, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 73, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(146−51, 146, 212)-Net over F₃ — Digital

Digital (95, 146, 212)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−51, 146, 2953)-Net in Base 3 — Upper bound on s

There is no (95, 146, 2954)-net in base 3, because

1 times m-reduction [i] would yield (95, 145, 2954)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1530 165938 313575 610090 474918 574230 751396 591838 749130 944841 583419 023269 > 3¹⁴⁵ [i]