MinT - Best Known (92−78, 92, s)-Nets in Base 16

Best Known (92−78, 92, s)-Nets in Base 16

(92−78, 92, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 92, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 92, 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]

(92−78, 92, 97)-Net over F₁₆ — Digital

Digital (14, 92, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 92, 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]

(92−78, 92, 689)-Net in Base 16 — Upper bound on s

There is no (14, 92, 690)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 618 482127 972976 852787 569770 730063 736550 145804 930777 474474 676811 894374 738980 568331 158477 318740 042494 761261 258776 > 16⁹² [i]