MinT - Best Known (86−73, 86, s)-Nets in Base 16

Best Known (86−73, 86, s)-Nets in Base 16

(86−73, 86, 65)-Net over F₁₆ — Constructive and digital

Digital (13, 86, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 86, 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]

(86−73, 86, 97)-Net over F₁₆ — Digital

Digital (13, 86, 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]

(86−73, 86, 643)-Net in Base 16 — Upper bound on s

There is no (13, 86, 644)-net in base 16, because

1 times m-reduction [i] would yield (13, 85, 644)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 296000 236022 328510 646571 542451 038293 357806 469738 206051 516180 496459 937281 247666 119789 744192 534181 327136 > 16⁸⁵ [i]