MinT - Best Known (228−132, 228, s)-Nets in Base 3

Best Known (228−132, 228, s)-Nets in Base 3

(228−132, 228, 64)-Net over F₃ — Constructive and digital

Digital (96, 228, 64)-net over F₃, using

t-expansion [i] based on digital (89, 228, 64)-net over F₃, using
- net from sequence [i] based on digital (89, 63)-sequence over F₃, using
  - base reduction for sequences [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]

(228−132, 228, 96)-Net over F₃ — Digital

Digital (96, 228, 96)-net over F₃, using

t-expansion [i] based on digital (89, 228, 96)-net over F₃, using
- net from sequence [i] based on digital (89, 95)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(228−132, 228, 502)-Net in Base 3 — Upper bound on s

There is no (96, 228, 503)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 223503 048558 723959 526132 326689 148516 908882 279574 906952 819469 024849 010595 564310 176845 333228 642365 570149 422061 > 3²²⁸ [i]