MinT - Best Known (96, 234, s)-Nets in Base 3

Best Known (96, 234, s)-Nets in Base 3

(96, 234, 64)-Net over F₃ — Constructive and digital

Digital (96, 234, 64)-net over F₃, using

t-expansion [i] based on digital (89, 234, 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]

(96, 234, 96)-Net over F₃ — Digital

Digital (96, 234, 96)-net over F₃, using

t-expansion [i] based on digital (89, 234, 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]

(96, 234, 485)-Net in Base 3 — Upper bound on s

There is no (96, 234, 486)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4863 288597 247407 834232 769618 299937 174847 857806 706073 833236 475491 553866 373197 454329 306847 860114 786043 948119 770661 > 3²³⁴ [i]