MinT - Best Known (109−90, 109, s)-Nets in Base 16

Best Known (109−90, 109, s)-Nets in Base 16

(109−90, 109, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 109, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 109, 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]

(109−90, 109, 129)-Net over F₁₆ — Digital

Digital (19, 109, 129)-net over F₁₆, using

net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(109−90, 109, 945)-Net in Base 16 — Upper bound on s

There is no (19, 109, 946)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 185342 884074 304546 016926 483708 843468 867640 160450 072955 971511 760497 104016 288763 743088 332326 419678 494372 060518 830249 261612 764508 325676 > 16¹⁰⁹ [i]