MinT - Best Known (82−66, 82, s)-Nets in Base 16

Best Known (82−66, 82, s)-Nets in Base 16

(82−66, 82, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 82, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 82, 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]

(82−66, 82, 98)-Net over F₁₆ — Digital

Digital (16, 82, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 82, 98)-net over F₁₆, using
- net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
    - a curve from the manYPoints database [i]

(82−66, 82, 843)-Net in Base 16 — Upper bound on s

There is no (16, 82, 844)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 556 931814 947106 447699 275136 778890 337850 628588 261394 329393 425866 082008 430199 828247 641038 381602 995406 > 16⁸² [i]