MinT - Best Known (13, 82, s)-Nets in Base 27

Best Known (13, 82, s)-Nets in Base 27

(13, 82, 96)-Net over F₂₇ — Constructive and digital

Digital (13, 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]

(13, 82, 136)-Net over F₂₇ — Digital

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]

(13, 82, 1320)-Net in Base 27 — Upper bound on s

There is no (13, 82, 1321)-net in base 27, because

1 times m-reduction [i] would yield (13, 81, 1321)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 88 464387 608775 464984 570584 928747 816403 076193 481694 190757 207538 014224 455053 413894 369321 955374 066118 527067 019418 790249 > 27⁸¹ [i]