MinT - Best Known (15, 15+32, s)-Nets in Base 27

Best Known (15, 15+32, s)-Nets in Base 27

(15, 15+32, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 47, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 47, 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+32, 116)-Net in Base 27 — Constructive

(15, 47, 116)-net in base 27, using

5 times m-reduction [i] based on (15, 52, 116)-net in base 27, using
- base change [i] based on digital (2, 39, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(15, 15+32, 136)-Net over F₂₇ — Digital

Digital (15, 47, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 47, 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+32, 4181)-Net in Base 27 — Upper bound on s

There is no (15, 47, 4182)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 18 817572 287488 138764 778231 888814 892305 371641 022899 059550 652541 338785 > 27⁴⁷ [i]