MinT - Best Known (90, 227, s)-Nets in Base 3

Best Known (90, 227, s)-Nets in Base 3

(90, 227, 64)-Net over F₃ — Constructive and digital

Digital (90, 227, 64)-net over F₃, using

t-expansion [i] based on digital (89, 227, 64)-net over F₃, using
- net from sequence [i] based on digital (89, 63)-sequence over F₃, using
  - base reduction for sequences [i] 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]

(90, 227, 96)-Net over F₃ — Digital

Digital (90, 227, 96)-net over F₃, using

t-expansion [i] based on digital (89, 227, 96)-net over F₃, using
- net from sequence [i] based on digital (89, 95)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(90, 227, 439)-Net in Base 3 — Upper bound on s

There is no (90, 227, 440)-net in base 3, because

1 times m-reduction [i] would yield (90, 226, 440)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 692220 176718 083182 466872 235715 724698 573387 345417 606982 137603 947629 771623 605615 207372 262661 057246 807219 990977 > 3²²⁶ [i]