MinT - Best Known (82−61, 82, s)-Nets in Base 16

Best Known (82−61, 82, s)-Nets in Base 16

(82−61, 82, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 82, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 82, 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]

(82−61, 82, 129)-Net over F₁₆ — Digital

Digital (21, 82, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 82, 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]

(82−61, 82, 1415)-Net in Base 16 — Upper bound on s

There is no (21, 82, 1416)-net in base 16, because

1 times m-reduction [i] would yield (21, 81, 1416)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 34 792352 961637 174770 887526 983562 346939 848764 866701 174924 928641 454695 612108 757816 147863 340841 422576 > 16⁸¹ [i]