MinT - Best Known (201−121, 201, s)-Nets in Base 3

Best Known (201−121, 201, s)-Nets in Base 3

(201−121, 201, 55)-Net over F₃ — Constructive and digital

Digital (80, 201, 55)-net over F₃, using

net from sequence [i] based on digital (80, 54)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 54)-sequence over F₉, using
  - s-reduction based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(201−121, 201, 84)-Net over F₃ — Digital

Digital (80, 201, 84)-net over F₃, using

t-expansion [i] based on digital (71, 201, 84)-net over F₃, using
- net from sequence [i] based on digital (71, 83)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(201−121, 201, 395)-Net in Base 3 — Upper bound on s

There is no (80, 201, 396)-net in base 3, because

1 times m-reduction [i] would yield (80, 200, 396)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 299401 011244 560897 805469 461469 599714 374292 120838 712664 100495 687661 010380 533244 098297 945360 474689 > 3²⁰⁰ [i]