MinT - Best Known (43, 43+48, s)-Nets in Base 27

Best Known (43, 43+48, s)-Nets in Base 27

(43, 43+48, 182)-Net over F₂₇ — Constructive and digital

Digital (43, 91, 182)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (9, 33, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]
2. digital (10, 58, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(43, 43+48, 370)-Net in Base 27 — Constructive

(43, 91, 370)-net in base 27, using

17 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(43, 43+48, 418)-Net over F₂₇ — Digital

Digital (43, 91, 418)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 43+48, 100830)-Net in Base 27 — Upper bound on s

There is no (43, 91, 100831)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 17955 460378 881622 274901 202246 168343 679345 024685 339535 892696 293402 387946 806932 991388 181054 368558 679161 794199 177931 972066 413467 111313 > 27⁹¹ [i]