MinT - Best Known (100, 100+120, s)-Nets in Base 3

Best Known (100, 100+120, s)-Nets in Base 3

(100, 100+120, 67)-Net over F₃ — Constructive and digital

Digital (100, 220, 67)-net over F₃, using

net from sequence [i] based on digital (100, 66)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 66)-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]

(100, 100+120, 96)-Net over F₃ — Digital

Digital (100, 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]

(100, 100+120, 593)-Net in Base 3 — Upper bound on s

There is no (100, 220, 594)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 933 679297 760214 321809 366018 513389 443187 019067 016408 117096 780262 623547 997889 344454 747487 250317 917220 961369 > 3²²⁰ [i]