MinT - Best Known (17, 84, s)-Nets in Base 27

Best Known (17, 84, s)-Nets in Base 27

(17, 84, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 84, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 84, 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, 84, 144)-Net over F₂₇ — Digital

Digital (17, 84, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 84, 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, 84, 1998)-Net in Base 27 — Upper bound on s

There is no (17, 84, 1999)-net in base 27, because

1 times m-reduction [i] would yield (17, 83, 1999)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 63870 789387 482026 108275 297399 644204 378756 298105 387308 776301 930417 402299 069540 636132 166892 115650 021250 007885 364775 434183 > 27⁸³ [i]