MinT - Best Known (15, 82, s)-Nets in Base 27

Best Known (15, 82, s)-Nets in Base 27

(15, 82, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 82, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 82, 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, 82, 136)-Net over F₂₇ — Digital

Digital (15, 82, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 82, 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, 82, 1633)-Net in Base 27 — Upper bound on s

There is no (15, 82, 1634)-net in base 27, because

1 times m-reduction [i] would yield (15, 81, 1634)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 87 715576 579637 783112 253477 852384 433812 374094 484620 492358 003294 939755 816346 383058 763124 994040 201022 015067 218934 938293 > 27⁸¹ [i]