MinT - Best Known (106−82, 106, s)-Nets in Base 16

Best Known (106−82, 106, s)-Nets in Base 16

(106−82, 106, 65)-Net over F₁₆ — Constructive and digital

Digital (24, 106, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 106, 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]

(106−82, 106, 129)-Net over F₁₆ — Digital

Digital (24, 106, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 106, 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]

(106−82, 106, 1373)-Net in Base 16 — Upper bound on s

There is no (24, 106, 1374)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 44 035242 840069 541832 135454 113184 961249 918394 506913 413781 679865 900047 019218 865508 764872 913042 654325 931288 447478 341722 156971 266886 > 16¹⁰⁶ [i]