MinT - Best Known (91−77, 91, s)-Nets in Base 27

Best Known (91−77, 91, s)-Nets in Base 27

(91−77, 91, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 91, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 91, 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]

(91−77, 91, 136)-Net over F₂₇ — Digital

Digital (14, 91, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 91, 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]

(91−77, 91, 1398)-Net in Base 27 — Upper bound on s

There is no (14, 91, 1399)-net in base 27, because

1 times m-reduction [i] would yield (14, 90, 1399)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 667 774031 849779 447176 655889 573397 266902 490330 628804 931733 242996 813649 410570 318715 910060 312407 708968 920171 228807 225526 663656 521301 > 27⁹⁰ [i]