MinT - Best Known (15, 15+77, s)-Nets in Base 27

Best Known (15, 15+77, s)-Nets in Base 27

(15, 15+77, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 92, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 92, 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]

(15, 15+77, 136)-Net over F₂₇ — Digital

Digital (15, 92, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 92, 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]

(15, 15+77, 1527)-Net in Base 27 — Upper bound on s

There is no (15, 92, 1528)-net in base 27, because

1 times m-reduction [i] would yield (15, 91, 1528)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 18228 340496 456760 751391 433464 271821 608623 906789 913447 891273 422549 432444 658902 582737 099655 845494 374137 898091 564961 215634 602116 896721 > 27⁹¹ [i]