MinT - Best Known (114, 114+113, s)-Nets in Base 3

Best Known (114, 114+113, s)-Nets in Base 3

(114, 114+113, 74)-Net over F₃ — Constructive and digital

Digital (114, 227, 74)-net over F₃, using

t-expansion [i] based on digital (107, 227, 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+113, 120)-Net over F₃ — Digital

Digital (114, 227, 120)-net over F₃, using

t-expansion [i] based on digital (113, 227, 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+113, 860)-Net in Base 3 — Upper bound on s

There is no (114, 227, 861)-net in base 3, because

1 times m-reduction [i] would yield (114, 226, 861)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 706588 464016 845928 378619 020724 880521 327561 777975 908230 520663 373607 513970 629456 536149 478615 975988 339166 935201 > 3²²⁶ [i]