MinT - Best Known (107, 107+124, s)-Nets in Base 3

Best Known (107, 107+124, s)-Nets in Base 3

(107, 107+124, 74)-Net over F₃ — Constructive and digital

Digital (107, 231, 74)-net over F₃, using

net from sequence [i] based on digital (107, 73)-sequence over F₃, using
- base reduction for sequences [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]

(107, 107+124, 104)-Net over F₃ — Digital

Digital (107, 231, 104)-net over F₃, using

t-expansion [i] based on digital (102, 231, 104)-net over F₃, using
- net from sequence [i] based on digital (102, 103)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 102 and N(F) ≥ 104, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(107, 107+124, 657)-Net in Base 3 — Upper bound on s

There is no (107, 231, 658)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 167 195812 603484 610632 035074 469366 449644 616170 254789 068291 617721 244962 854885 514115 028458 636111 890749 119826 489037 > 3²³¹ [i]