MinT - Best Known (222−134, 222, s)-Nets in Base 3

Best Known (222−134, 222, s)-Nets in Base 3

(222−134, 222, 63)-Net over F₃ — Constructive and digital

Digital (88, 222, 63)-net over F₃, using

net from sequence [i] based on digital (88, 62)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 62)-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]

(222−134, 222, 84)-Net over F₃ — Digital

Digital (88, 222, 84)-net over F₃, using

t-expansion [i] based on digital (71, 222, 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]

(222−134, 222, 428)-Net in Base 3 — Upper bound on s

There is no (88, 222, 429)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9320 068512 026634 027643 199867 634366 535122 797419 009048 799083 606284 113995 358632 512712 351894 180021 175757 036363 > 3²²² [i]