MinT - Best Known (219−90, 219, s)-Nets in Base 3

Best Known (219−90, 219, s)-Nets in Base 3

(219−90, 219, 148)-Net over F₃ — Constructive and digital

Digital (129, 219, 148)-net over F₃, using

5 times m-reduction [i] based on digital (129, 224, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 112, 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]

(219−90, 219, 187)-Net over F₃ — Digital

Digital (129, 219, 187)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−90, 219, 1805)-Net in Base 3 — Upper bound on s

There is no (129, 219, 1806)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 310 377755 460213 101974 780013 989257 230817 435643 395638 861339 023290 307712 837427 229444 700622 350657 107938 189669 > 3²¹⁹ [i]