MinT - Best Known (88, 188, s)-Nets in Base 3

Best Known (88, 188, s)-Nets in Base 3

(88, 188, 63)-Net over F₃ — Constructive and digital

Digital (88, 188, 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]

(88, 188, 84)-Net over F₃ — Digital

Digital (88, 188, 84)-net over F₃, using

t-expansion [i] based on digital (71, 188, 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]

(88, 188, 558)-Net in Base 3 — Upper bound on s

There is no (88, 188, 559)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 529504 428044 906558 911404 725606 011780 276039 074629 033001 308283 219619 274335 195237 848326 730237 > 3¹⁸⁸ [i]