MinT - Best Known (153, 228, s)-Nets in Base 3

Best Known (153, 228, s)-Nets in Base 3

(153, 228, 164)-Net over F₃ — Constructive and digital

Digital (153, 228, 164)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (7, 44, 16)-net over F₃, using
  - net from sequence [i] based on digital (7, 15)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 7 and N(F) ≥ 16, using
      - an explicitly constructive algebraic function field [i]
2. digital (109, 184, 148)-net over F₃, using
  - trace code for nets [i] based on digital (17, 92, 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]

(153, 228, 371)-Net over F₃ — Digital

Digital (153, 228, 371)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(153, 228, 6159)-Net in Base 3 — Upper bound on s

There is no (153, 228, 6160)-net in base 3, because

1 times m-reduction [i] would yield (153, 227, 6160)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 034977 675411 093471 731098 936219 626093 520029 470426 879529 683628 772389 658766 544206 219486 106689 259133 294664 238625 > 3²²⁷ [i]