MinT - Best Known (80−67, 80, s)-Nets in Base 27

Best Known (80−67, 80, s)-Nets in Base 27

(80−67, 80, 96)-Net over F₂₇ — Constructive and digital

Digital (13, 80, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 80, 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]

(80−67, 80, 136)-Net over F₂₇ — Digital

Digital (13, 80, 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]

(80−67, 80, 1334)-Net in Base 27 — Upper bound on s

There is no (13, 80, 1335)-net in base 27, because

1 times m-reduction [i] would yield (13, 79, 1335)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 120226 450081 784049 067768 613657 423969 507815 974475 036013 388669 725648 434387 280757 380351 353694 777208 320916 084656 437335 > 27⁷⁹ [i]