MinT - Best Known (190−87, 190, s)-Nets in Base 3

Best Known (190−87, 190, s)-Nets in Base 3

(190−87, 190, 80)-Net over F₃ — Constructive and digital

Digital (103, 190, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 95, 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]

(190−87, 190, 122)-Net over F₃ — Digital

Digital (103, 190, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−87, 190, 1013)-Net in Base 3 — Upper bound on s

There is no (103, 190, 1014)-net in base 3, because

1 times m-reduction [i] would yield (103, 189, 1014)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 503773 866379 876530 124813 295262 875830 293370 086852 468493 545030 357267 870573 394630 093071 618065 > 3¹⁸⁹ [i]