MinT - Best Known (240−134, 240, s)-Nets in Base 3

Best Known (240−134, 240, s)-Nets in Base 3

(240−134, 240, 73)-Net over F₃ — Constructive and digital

Digital (106, 240, 73)-net over F₃, using

net from sequence [i] based on digital (106, 72)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 72)-sequence over F₉, using
  - s-reduction 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]

(240−134, 240, 104)-Net over F₃ — Digital

Digital (106, 240, 104)-net over F₃, using

t-expansion [i] based on digital (102, 240, 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]

(240−134, 240, 595)-Net in Base 3 — Upper bound on s

There is no (106, 240, 596)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 236334 041950 190247 725261 101480 007030 119374 684054 551028 402336 044690 356954 210034 405719 106784 448164 977352 846191 561073 > 3²⁴⁰ [i]