MinT - Best Known (106−85, 106, s)-Nets in Base 16

Best Known (106−85, 106, s)-Nets in Base 16

(106−85, 106, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 106, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 106, 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]

(106−85, 106, 129)-Net over F₁₆ — Digital

Digital (21, 106, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 106, 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]

(106−85, 106, 1104)-Net in Base 16 — Upper bound on s

There is no (21, 106, 1105)-net in base 16, because

1 times m-reduction [i] would yield (21, 105, 1105)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 805878 376658 331250 962772 732233 468794 286806 892490 461495 582717 087951 899902 729372 764771 335899 677543 282895 050501 214525 721337 225776 > 16¹⁰⁵ [i]