MinT - Best Known (94, 244, s)-Nets in Base 3

Best Known (94, 244, s)-Nets in Base 3

(94, 244, 64)-Net over F₃ — Constructive and digital

Digital (94, 244, 64)-net over F₃, using

t-expansion [i] based on digital (89, 244, 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]

(94, 244, 96)-Net over F₃ — Digital

Digital (94, 244, 96)-net over F₃, using

t-expansion [i] based on digital (89, 244, 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]

(94, 244, 442)-Net in Base 3 — Upper bound on s

There is no (94, 244, 443)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 289 807830 643085 595873 365487 948708 791872 457634 658930 104386 875523 789134 348164 181055 250945 309994 086758 317167 905819 762811 > 3²⁴⁴ [i]