MinT - Best Known (228−95, 228, s)-Nets in Base 3

Best Known (228−95, 228, s)-Nets in Base 3

(228−95, 228, 148)-Net over F₃ — Constructive and digital

Digital (133, 228, 148)-net over F₃, using

4 times m-reduction [i] based on digital (133, 232, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 116, 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]

(228−95, 228, 187)-Net over F₃ — Digital

Digital (133, 228, 187)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−95, 228, 1805)-Net in Base 3 — Upper bound on s

There is no (133, 228, 1806)-net in base 3, because

1 times m-reduction [i] would yield (133, 227, 1806)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 065775 384963 285475 571637 990523 998282 320033 609802 858617 278834 175015 502087 424619 043388 291137 391828 958771 714281 > 3²²⁷ [i]