MinT - Best Known (15, 86, s)-Nets in Base 27

Best Known (15, 86, s)-Nets in Base 27

(15, 86, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 86, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 86, 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]

(15, 86, 136)-Net over F₂₇ — Digital

Digital (15, 86, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 86, 136)-net over F₂₇, using
- net from sequence [i] based on digital (13, 135)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 13 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(15, 86, 1582)-Net in Base 27 — Upper bound on s

There is no (15, 86, 1583)-net in base 27, because

1 times m-reduction [i] would yield (15, 85, 1583)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 46 384737 102077 409394 265767 757716 366904 794553 893789 041642 544965 722563 548322 016339 792126 801398 828327 647989 635958 828449 874355 > 27⁸⁵ [i]