MinT - Best Known (66, 66+50, s)-Nets in Base 9

Best Known (66, 66+50, s)-Nets in Base 9

(66, 66+50, 344)-Net over F₉ — Constructive and digital

Digital (66, 116, 344)-net over F₉, using

2 times m-reduction [i] based on digital (66, 118, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 59, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(66, 66+50, 452)-Net over F₉ — Digital

Digital (66, 116, 452)-net over F₉, using

trace code for nets [i] based on digital (8, 58, 226)-net over F₈₁, using
- net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
    - a curve from the manYPoints database [i]

(66, 66+50, 34043)-Net in Base 9 — Upper bound on s

There is no (66, 116, 34044)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 492 538881 439375 420285 468923 652217 491828 782415 547406 477052 297775 973626 605254 826196 182699 508539 520682 085004 601057 > 9¹¹⁶ [i]