MinT - Best Known (98, 98+126, s)-Nets in Base 3

Best Known (98, 98+126, s)-Nets in Base 3

(98, 98+126, 65)-Net over F₃ — Constructive and digital

Digital (98, 224, 65)-net over F₃, using

net from sequence [i] based on digital (98, 64)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 64)-sequence over F₉, using
  - s-reduction 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]

(98, 98+126, 96)-Net over F₃ — Digital

Digital (98, 224, 96)-net over F₃, using

t-expansion [i] based on digital (89, 224, 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]

(98, 98+126, 544)-Net in Base 3 — Upper bound on s

There is no (98, 224, 545)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 82437 611910 646759 965291 623795 101947 815774 146412 828792 691690 201633 412663 934861 316965 632539 310157 056250 008107 > 3²²⁴ [i]