MinT - Best Known (17, 17+24, s)-Nets in Base 27

Best Known (17, 17+24, s)-Nets in Base 27

(17, 17+24, 102)-Net over F₂₇ — Constructive and digital

Digital (17, 41, 102)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (1, 13, 38)-net over F₂₇, using
  - net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]
2. digital (4, 28, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(17, 17+24, 144)-Net over F₂₇ — Digital

Digital (17, 41, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 41, 144)-net over F₂₇, using
- net from sequence [i] based on digital (16, 143)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 16 and N(F) ≥ 144, using
    - a curve from the manYPoints database [i]

(17, 17+24, 160)-Net in Base 27 — Constructive

(17, 41, 160)-net in base 27, using

7 times m-reduction [i] based on (17, 48, 160)-net in base 27, using
- base change [i] based on digital (5, 36, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(17, 17+24, 190)-Net in Base 27

(17, 41, 190)-net in base 27, using

3 times m-reduction [i] based on (17, 44, 190)-net in base 27, using
- base change [i] based on digital (6, 33, 190)-net over F₈₁, using
  - net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
      - a curve from the manYPoints database [i]

(17, 17+24, 15802)-Net in Base 27 — Upper bound on s

There is no (17, 41, 15803)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 48549 319480 440982 673768 923074 644028 690539 209904 156981 197737 > 27⁴¹ [i]