MinT - Best Known (16, 16+65, s)-Nets in Base 16

Best Known (16, 16+65, s)-Nets in Base 16

(16, 16+65, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 81, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 81, 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]

(16, 16+65, 98)-Net over F₁₆ — Digital

Digital (16, 81, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 81, 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]

(16, 16+65, 855)-Net in Base 16 — Upper bound on s

There is no (16, 81, 856)-net in base 16, because

1 times m-reduction [i] would yield (16, 80, 856)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 167067 374450 814769 206650 089257 400505 786794 885628 188207 718746 277104 129093 173540 195977 697668 950106 > 16⁸⁰ [i]