MinT - Best Known (13, 13+57, s)-Nets in Base 27

Best Known (13, 13+57, s)-Nets in Base 27

(13, 13+57, 96)-Net over F₂₇ — Constructive and digital

Digital (13, 70, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 70, 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, 13+57, 136)-Net over F₂₇ — Digital

Digital (13, 70, 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, 13+57, 1448)-Net in Base 27 — Upper bound on s

There is no (13, 70, 1449)-net in base 27, because

1 times m-reduction [i] would yield (13, 69, 1449)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 584 087651 522069 705291 517320 669603 858716 978016 969436 700283 784713 620922 464478 951492 284411 703279 301457 > 27⁶⁹ [i]