MinT - Best Known (107−92, 107, s)-Nets in Base 16

Best Known (107−92, 107, s)-Nets in Base 16

(107−92, 107, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 107, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 107, 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]

(107−92, 107, 98)-Net over F₁₆ — Digital

Digital (15, 107, 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]

(107−92, 107, 733)-Net in Base 16 — Upper bound on s

There is no (15, 107, 734)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 724 621773 345211 205677 679676 809538 051407 631083 738358 922020 699661 063929 410343 294492 254345 844157 857102 081817 525509 917238 734975 248336 > 16¹⁰⁷ [i]