MinT - Best Known (170−96, 170, s)-Nets in Base 3

Best Known (170−96, 170, s)-Nets in Base 3

(170−96, 170, 49)-Net over F₃ — Constructive and digital

Digital (74, 170, 49)-net over F₃, using

net from sequence [i] based on digital (74, 48)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 48)-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]

(170−96, 170, 84)-Net over F₃ — Digital

Digital (74, 170, 84)-net over F₃, using

t-expansion [i] based on digital (71, 170, 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]

(170−96, 170, 413)-Net in Base 3 — Upper bound on s

There is no (74, 170, 414)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1406 193285 039092 115466 385478 654803 909996 919844 868530 587089 482742 165824 568181 888225 > 3¹⁷⁰ [i]