MinT - Best Known (17, 108, s)-Nets in Base 27

Best Known (17, 108, s)-Nets in Base 27

(17, 108, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 108, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 108, 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]

(17, 108, 144)-Net over F₂₇ — Digital

Digital (17, 108, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 108, 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]

(17, 108, 1692)-Net in Base 27 — Upper bound on s

There is no (17, 108, 1693)-net in base 27, because

1 times m-reduction [i] would yield (17, 107, 1693)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1434 723580 511423 046428 667012 198678 593335 043924 481257 944879 028457 308146 705386 059115 728420 934944 802402 535831 588361 156052 323652 990409 934506 852813 667396 035843 > 27¹⁰⁷ [i]