MinT - Best Known (192−87, 192, s)-Nets in Base 3

Best Known (192−87, 192, s)-Nets in Base 3

(192−87, 192, 80)-Net over F₃ — Constructive and digital

Digital (105, 192, 80)-net over F₃, using

2 times m-reduction [i] based on digital (105, 194, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 97, 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]

(192−87, 192, 127)-Net over F₃ — Digital

Digital (105, 192, 127)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−87, 192, 1069)-Net in Base 3 — Upper bound on s

There is no (105, 192, 1070)-net in base 3, because

1 times m-reduction [i] would yield (105, 191, 1070)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 896181 141139 609144 605725 569195 556317 577031 209191 696805 411480 249869 388355 096377 921374 450865 > 3¹⁹¹ [i]