MinT - Best Known (114, 114+136, s)-Nets in Base 3

Best Known (114, 114+136, s)-Nets in Base 3

(114, 114+136, 74)-Net over F₃ — Constructive and digital

Digital (114, 250, 74)-net over F₃, using

t-expansion [i] based on digital (107, 250, 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]

(114, 114+136, 120)-Net over F₃ — Digital

Digital (114, 250, 120)-net over F₃, using

t-expansion [i] based on digital (113, 250, 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]

(114, 114+136, 677)-Net in Base 3 — Upper bound on s

There is no (114, 250, 678)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 202051 870211 778454 517422 496128 959871 261754 635166 340313 662279 158990 043762 162983 602681 895292 661301 743908 218575 732288 383369 > 3²⁵⁰ [i]