MinT - Best Known (217−93, 217, s)-Nets in Base 3

Best Known (217−93, 217, s)-Nets in Base 3

(217−93, 217, 128)-Net over F₃ — Constructive and digital

Digital (124, 217, 128)-net over F₃, using

5 times m-reduction [i] based on digital (124, 222, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 111, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(217−93, 217, 165)-Net over F₃ — Digital

Digital (124, 217, 165)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−93, 217, 1520)-Net in Base 3 — Upper bound on s

There is no (124, 217, 1521)-net in base 3, because

1 times m-reduction [i] would yield (124, 216, 1521)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 659582 891053 766384 823321 159673 342652 715865 838493 220329 314012 461639 128846 833970 798493 036867 715108 449369 > 3²¹⁶ [i]