MinT - Best Known (74−59, 74, s)-Nets in Base 27

Best Known (74−59, 74, s)-Nets in Base 27

(74−59, 74, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 74, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 74, 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]

(74−59, 74, 136)-Net over F₂₇ — Digital

Digital (15, 74, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 74, 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]

(74−59, 74, 1784)-Net in Base 27 — Upper bound on s

There is no (15, 74, 1785)-net in base 27, because

1 times m-reduction [i] would yield (15, 73, 1785)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 309 884251 719664 261736 261233 673027 806265 526778 430070 764591 757118 440549 711927 858847 331272 592476 723175 938683 > 27⁷³ [i]