MinT - Best Known (17, 17+55, s)-Nets in Base 27

Best Known (17, 17+55, s)-Nets in Base 27

(17, 17+55, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 72, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 72, 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+55, 144)-Net over F₂₇ — Digital

Digital (17, 72, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 72, 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+55, 2425)-Net in Base 27 — Upper bound on s

There is no (17, 72, 2426)-net in base 27, because

1 times m-reduction [i] would yield (17, 71, 2426)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 423565 420185 589932 377044 244153 772029 281153 421777 275173 855872 678682 182363 305190 025565 435698 605660 909041 > 27⁷¹ [i]