MinT - Best Known (87−67, 87, s)-Nets in Base 16

Best Known (87−67, 87, s)-Nets in Base 16

(87−67, 87, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 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]

(87−67, 87, 129)-Net over F₁₆ — Digital

Digital (20, 87, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 87, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(87−67, 87, 1187)-Net in Base 16 — Upper bound on s

There is no (20, 87, 1188)-net in base 16, because

1 times m-reduction [i] would yield (20, 86, 1188)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 36 170175 951799 564304 756250 647330 906112 724686 244272 428718 292994 093060 469848 104859 096866 219393 637010 396361 > 16⁸⁶ [i]