MinT - Best Known (15, 15+57, s)-Nets in Base 27

Best Known (15, 15+57, s)-Nets in Base 27

(15, 15+57, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 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]

(15, 15+57, 136)-Net over F₂₇ — Digital

Digital (15, 72, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 72, 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, 15+57, 1837)-Net in Base 27 — Upper bound on s

There is no (15, 72, 1838)-net in base 27, because

1 times m-reduction [i] would yield (15, 71, 1838)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 429219 153067 747789 585505 744853 927736 963295 504321 710071 526742 086151 349993 505468 876087 707477 404146 707065 > 27⁷¹ [i]