MinT - Best Known (22, 86, s)-Nets in Base 16

Best Known (22, 86, s)-Nets in Base 16

(22, 86, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 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]

(22, 86, 129)-Net over F₁₆ — Digital

Digital (22, 86, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 86, 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]

(22, 86, 1450)-Net in Base 16 — Upper bound on s

There is no (22, 86, 1451)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 35 931598 583358 344496 459028 147861 724609 943640 161958 588594 343170 011707 211998 247549 735106 328754 298458 028081 > 16⁸⁶ [i]