MinT - Best Known (96−79, 96, s)-Nets in Base 27

Best Known (96−79, 96, s)-Nets in Base 27

(96−79, 96, 96)-Net over F₂₇ — Constructive and digital

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

t-expansion [i] based on digital (11, 96, 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]

(96−79, 96, 144)-Net over F₂₇ — Digital

Digital (17, 96, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 96, 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]

(96−79, 96, 1795)-Net in Base 27 — Upper bound on s

There is no (17, 96, 1796)-net in base 27, because

1 times m-reduction [i] would yield (17, 95, 1796)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 9640 071265 091533 795981 122427 059682 593038 329098 759667 056786 964165 812225 143789 578534 466122 269072 047513 540392 768283 019443 527148 202984 122193 > 27⁹⁵ [i]