MinT - Best Known (105−88, 105, s)-Nets in Base 16

Best Known (105−88, 105, s)-Nets in Base 16

(105−88, 105, 65)-Net over F₁₆ — Constructive and digital

Digital (17, 105, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 105, 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]

(105−88, 105, 112)-Net over F₁₆ — Digital

Digital (17, 105, 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]

(105−88, 105, 835)-Net in Base 16 — Upper bound on s

There is no (17, 105, 836)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 800185 562884 827251 873855 358602 370164 500287 933584 354557 313379 352932 624535 866169 396993 712022 366803 899012 796534 376305 522789 182736 > 16¹⁰⁵ [i]