MinT - Best Known (86−74, 86, s)-Nets in Base 16

Best Known (86−74, 86, s)-Nets in Base 16

(86−74, 86, 65)-Net over F₁₆ — Constructive and digital

Digital (12, 86, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 86, 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]

(86−74, 86, 88)-Net over F₁₆ — Digital

Digital (12, 86, 88)-net over F₁₆, using

net from sequence [i] based on digital (12, 87)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 12 and N(F) ≥ 88, using
  - a curve from the manYPoints database [i]

(86−74, 86, 594)-Net in Base 16 — Upper bound on s

There is no (12, 86, 595)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 37 395616 879950 704770 124732 389470 071223 652502 162031 491606 010909 183038 536363 445479 750891 909928 514451 164976 > 16⁸⁶ [i]