MinT - Best Known (116, 116+119, s)-Nets in Base 3

Best Known (116, 116+119, s)-Nets in Base 3

(116, 116+119, 74)-Net over F₃ — Constructive and digital

Digital (116, 235, 74)-net over F₃, using

t-expansion [i] based on digital (107, 235, 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]

(116, 116+119, 120)-Net over F₃ — Digital

Digital (116, 235, 120)-net over F₃, using

t-expansion [i] based on digital (113, 235, 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]

(116, 116+119, 833)-Net in Base 3 — Upper bound on s

There is no (116, 235, 834)-net in base 3, because

1 times m-reduction [i] would yield (116, 234, 834)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4573 261336 065561 705811 310067 244296 484989 074274 755582 390499 276234 277396 864415 617678 552006 852800 247521 878188 163745 > 3²³⁴ [i]