MinT - Best Known (190−75, 190, s)-Nets in Base 3

Best Known (190−75, 190, s)-Nets in Base 3

(190−75, 190, 148)-Net over F₃ — Constructive and digital

Digital (115, 190, 148)-net over F₃, using

6 times m-reduction [i] based on digital (115, 196, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 98, 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]

(190−75, 190, 186)-Net over F₃ — Digital

Digital (115, 190, 186)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−75, 190, 1968)-Net in Base 3 — Upper bound on s

There is no (115, 190, 1969)-net in base 3, because

1 times m-reduction [i] would yield (115, 189, 1969)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 511508 671195 940878 677323 244363 401925 407907 580166 071608 694123 912870 789404 766930 565668 760531 > 3¹⁸⁹ [i]