MinT - Best Known (189−75, 189, s)-Nets in Base 3

Best Known (189−75, 189, s)-Nets in Base 3

(189−75, 189, 148)-Net over F₃ — Constructive and digital

Digital (114, 189, 148)-net over F₃, using

5 times m-reduction [i] based on digital (114, 194, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 97, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(189−75, 189, 182)-Net over F₃ — Digital

Digital (114, 189, 182)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−75, 189, 1909)-Net in Base 3 — Upper bound on s

There is no (114, 189, 1910)-net in base 3, because

1 times m-reduction [i] would yield (114, 188, 1910)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 500553 301453 132388 380759 991669 142076 119853 610499 560339 563318 618256 815773 509969 063001 390085 > 3¹⁸⁸ [i]