MinT - Best Known (17, 17+38, s)-Nets in Base 27

Best Known (17, 17+38, s)-Nets in Base 27

(17, 17+38, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 55, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 55, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(17, 17+38, 116)-Net in Base 27 — Constructive

(17, 55, 116)-net in base 27, using

5 times m-reduction [i] based on (17, 60, 116)-net in base 27, using
- base change [i] based on digital (2, 45, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(17, 17+38, 144)-Net over F₂₇ — Digital

Digital (17, 55, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 55, 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+38, 4233)-Net in Base 27 — Upper bound on s

There is no (17, 55, 4234)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 5 328410 075109 592367 556128 994334 762757 704680 274082 206670 044121 938369 320812 484225 > 27⁵⁵ [i]