MinT - Best Known (15, 15+78, s)-Nets in Base 27

Best Known (15, 15+78, s)-Nets in Base 27

(15, 15+78, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 93, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 93, 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+78, 136)-Net over F₂₇ — Digital

Digital (15, 93, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 93, 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+78, 1513)-Net in Base 27 — Upper bound on s

There is no (15, 93, 1514)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 13 378814 838096 577016 916807 099882 388867 663823 193489 717338 552670 502476 056849 976974 358934 757753 354736 697924 393357 428163 502336 132789 336697 > 27⁹³ [i]