MinT - Best Known (17, 17+43, s)-Nets in Base 27

Best Known (17, 17+43, s)-Nets in Base 27

(17, 17+43, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 60, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 60, 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+43, 116)-Net in Base 27 — Constructive

(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+43, 144)-Net over F₂₇ — Digital

Digital (17, 60, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 60, 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+43, 3496)-Net in Base 27 — Upper bound on s

There is no (17, 60, 3497)-net in base 27, because

1 times m-reduction [i] would yield (17, 59, 3497)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2 830270 215122 903336 605230 296573 698299 812902 103021 571563 737936 503172 475576 099481 589563 > 27⁵⁹ [i]