MinT - Best Known (87−73, 87, s)-Nets in Base 16

Best Known (87−73, 87, s)-Nets in Base 16

(87−73, 87, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 87, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 87, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(87−73, 87, 97)-Net over F₁₆ — Digital

Digital (14, 87, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 87, 97)-net over F₁₆, using
- net from sequence [i] based on digital (13, 96)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 13 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(87−73, 87, 696)-Net in Base 16 — Upper bound on s

There is no (14, 87, 697)-net in base 16, because

1 times m-reduction [i] would yield (14, 86, 697)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 36 498730 275378 793349 454589 636312 192290 829958 001105 063572 113927 870171 889382 026804 119784 007719 875408 501006 > 16⁸⁶ [i]