MinT - Best Known (16, 16+40, s)-Nets in Base 16

Best Known (16, 16+40, s)-Nets in Base 16

(16, 16+40, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 56, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 56, 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+40, 98)-Net over F₁₆ — Digital

Digital (16, 56, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 56, 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+40, 1291)-Net in Base 16 — Upper bound on s

There is no (16, 56, 1292)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 27 122138 909525 834762 675905 615115 927519 685261 672677 275454 887785 258976 > 16⁵⁶ [i]