MinT - Best Known (90−75, 90, s)-Nets in Base 27

Best Known (90−75, 90, s)-Nets in Base 27

(90−75, 90, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 90, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 90, 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]

(90−75, 90, 136)-Net over F₂₇ — Digital

Digital (15, 90, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 90, 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]

(90−75, 90, 1543)-Net in Base 27 — Upper bound on s

There is no (15, 90, 1544)-net in base 27, because

1 times m-reduction [i] would yield (15, 89, 1544)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 24 863366 823725 966122 988094 128862 800022 576578 552623 136266 687528 402910 288547 237477 676817 634597 041861 001363 523857 077634 116396 562513 > 27⁸⁹ [i]