MinT - Best Known (97, 97+123, s)-Nets in Base 3

Best Known (97, 97+123, s)-Nets in Base 3

(97, 97+123, 64)-Net over F₃ — Constructive and digital

Digital (97, 220, 64)-net over F₃, using

t-expansion [i] based on digital (89, 220, 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]

(97, 97+123, 96)-Net over F₃ — Digital

Digital (97, 220, 96)-net over F₃, using

t-expansion [i] based on digital (89, 220, 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]

(97, 97+123, 550)-Net in Base 3 — Upper bound on s

There is no (97, 220, 551)-net in base 3, because

1 times m-reduction [i] would yield (97, 219, 551)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 334 511878 386468 246828 757211 922797 138830 107255 416766 499444 184093 652567 032776 154619 573658 590810 108528 925719 > 3²¹⁹ [i]