MinT - Best Known (48−36, 48, s)-Nets in Base 16

Best Known (48−36, 48, s)-Nets in Base 16

(48−36, 48, 65)-Net over F₁₆ — Constructive and digital

Digital (12, 48, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 48, 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]

(48−36, 48, 88)-Net over F₁₆ — Digital

Digital (12, 48, 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]

(48−36, 48, 808)-Net in Base 16 — Upper bound on s

There is no (12, 48, 809)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6298 903078 274923 944790 066086 047088 294053 090382 707515 070056 > 16⁴⁸ [i]