MinT - Best Known (115, 115+119, s)-Nets in Base 3

Best Known (115, 115+119, s)-Nets in Base 3

(115, 115+119, 74)-Net over F₃ — Constructive and digital

Digital (115, 234, 74)-net over F₃, using

t-expansion [i] based on digital (107, 234, 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]

(115, 115+119, 120)-Net over F₃ — Digital

Digital (115, 234, 120)-net over F₃, using

t-expansion [i] based on digital (113, 234, 120)-net over F₃, using
- net from sequence [i] based on digital (113, 119)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 113 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(115, 115+119, 817)-Net in Base 3 — Upper bound on s

There is no (115, 234, 818)-net in base 3, because

1 times m-reduction [i] would yield (115, 233, 818)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1567 087693 791355 055811 906069 056013 825320 248987 377664 665625 288042 594381 906338 858370 870206 027550 332146 713747 859937 > 3²³³ [i]