MinT - Best Known (110, 110+127, s)-Nets in Base 3

Best Known (110, 110+127, s)-Nets in Base 3

(110, 110+127, 74)-Net over F₃ — Constructive and digital

Digital (110, 237, 74)-net over F₃, using

t-expansion [i] based on digital (107, 237, 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]

(110, 110+127, 104)-Net over F₃ — Digital

Digital (110, 237, 104)-net over F₃, using

t-expansion [i] based on digital (102, 237, 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]

(110, 110+127, 684)-Net in Base 3 — Upper bound on s

There is no (110, 237, 685)-net in base 3, because

1 times m-reduction [i] would yield (110, 236, 685)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 42523 795892 298173 089070 353473 779574 799034 936213 227596 605791 753289 775696 200931 642470 510301 508581 034884 580634 251227 > 3²³⁶ [i]