MinT - Best Known (94−77, 94, s)-Nets in Base 27

Best Known (94−77, 94, s)-Nets in Base 27

(94−77, 94, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 94, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 94, 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]

(94−77, 94, 144)-Net over F₂₇ — Digital

Digital (17, 94, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 94, 144)-net over F₂₇, using
- net from sequence [i] based on digital (16, 143)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 16 and N(F) ≥ 144, using
    - a curve from the manYPoints database [i]

(94−77, 94, 1820)-Net in Base 27 — Upper bound on s

There is no (17, 94, 1821)-net in base 27, because

1 times m-reduction [i] would yield (17, 93, 1821)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 13 235409 005664 847880 052634 630432 852734 674553 261792 533007 185461 475373 340612 309904 791296 172815 704395 487315 972151 821134 455813 086531 450017 > 27⁹³ [i]