MinT - Best Known (82−67, 82, s)-Nets in Base 16

Best Known (82−67, 82, s)-Nets in Base 16

(82−67, 82, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 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]

(82−67, 82, 98)-Net over F₁₆ — Digital

Digital (15, 82, 98)-net over F₁₆, using

net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(82−67, 82, 774)-Net in Base 16 — Upper bound on s

There is no (15, 82, 775)-net in base 16, because

1 times m-reduction [i] would yield (15, 81, 775)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 35 487813 334976 868370 011528 604265 026749 089311 906945 947149 683205 156914 783267 997666 151507 087621 087376 > 16⁸¹ [i]