MinT - Best Known (95−79, 95, s)-Nets in Base 27

Best Known (95−79, 95, s)-Nets in Base 27

(95−79, 95, 96)-Net over F₂₇ — Constructive and digital

Digital (16, 95, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 95, 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]

(95−79, 95, 144)-Net over F₂₇ — Digital

Digital (16, 95, 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]

(95−79, 95, 1648)-Net in Base 27 — Upper bound on s

There is no (16, 95, 1649)-net in base 27, because

1 times m-reduction [i] would yield (16, 94, 1649)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 358 659779 818173 042958 676213 457748 966294 874048 342645 587504 206100 225568 304669 005984 055859 048889 771765 856264 627972 175017 012472 461371 208819 > 27⁹⁴ [i]