MinT - Best Known (142−63, 142, s)-Nets in Base 3

Best Known (142−63, 142, s)-Nets in Base 3

(142−63, 142, 80)-Net over F₃ — Constructive and digital

Digital (79, 142, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 71, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(142−63, 142, 105)-Net over F₃ — Digital

Digital (79, 142, 105)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−63, 142, 888)-Net in Base 3 — Upper bound on s

There is no (79, 142, 889)-net in base 3, because

1 times m-reduction [i] would yield (79, 141, 889)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19 095480 461037 673280 773406 854457 542445 743741 715262 481221 336796 845579 > 3¹⁴¹ [i]