MinT - Best Known (119−102, 119, s)-Nets in Base 16

Best Known (119−102, 119, s)-Nets in Base 16

(119−102, 119, 65)-Net over F₁₆ — Constructive and digital

Digital (17, 119, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 119, 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]

(119−102, 119, 112)-Net over F₁₆ — Digital

Digital (17, 119, 112)-net over F₁₆, using

net from sequence [i] based on digital (17, 111)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 17 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(119−102, 119, 825)-Net in Base 16 — Upper bound on s

There is no (17, 119, 826)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 198952 766173 273078 572439 724340 463099 971727 055983 048822 861819 095751 384152 083863 675169 007347 933361 426758 892074 353647 307343 355256 468461 631100 812516 > 16¹¹⁹ [i]