MinT - Best Known (97−56, 97, s)-Nets in Base 27

Best Known (97−56, 97, s)-Nets in Base 27

(97−56, 97, 158)-Net over F₂₇ — Constructive and digital

Digital (41, 97, 158)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (6, 34, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]
2. digital (7, 63, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(97−56, 97, 273)-Net over F₂₇ — Digital

Digital (41, 97, 273)-net over F₂₇, using

t-expansion [i] based on digital (40, 97, 273)-net over F₂₇, using
- net from sequence [i] based on digital (40, 272)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 40 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(97−56, 97, 370)-Net in Base 27 — Constructive

(41, 97, 370)-net in base 27, using

3 times m-reduction [i] based on (41, 100, 370)-net in base 27, using
- base change [i] based on digital (16, 75, 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]

(97−56, 97, 39493)-Net in Base 27 — Upper bound on s

There is no (41, 97, 39494)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 6 957791 058880 017954 280130 432449 969685 242028 362006 694722 045516 691370 412672 603391 613466 376018 751442 460773 187625 939934 125399 779706 251622 045433 > 27⁹⁷ [i]