MinT - Best Known (106−89, 106, s)-Nets in Base 27

Best Known (106−89, 106, s)-Nets in Base 27

(106−89, 106, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 106, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 106, 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]

(106−89, 106, 144)-Net over F₂₇ — Digital

Digital (17, 106, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 106, 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]

(106−89, 106, 1705)-Net in Base 27 — Upper bound on s

There is no (17, 106, 1706)-net in base 27, because

1 times m-reduction [i] would yield (17, 105, 1706)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 988741 123109 225796 067100 340636 345263 118888 137685 599052 706265 791753 264655 670589 292716 545851 473378 983433 960228 452966 904491 788661 690459 166736 708657 737145 > 27¹⁰⁵ [i]