MinT - Best Known (106−63, 106, s)-Nets in Base 16

Best Known (106−63, 106, s)-Nets in Base 16

(106−63, 106, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 106, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 106, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(106−63, 106, 226)-Net over F₁₆ — Digital

Digital (43, 106, 226)-net over F₁₆, using

net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
  - Drinfeld modules of rank 1 [i]

(106−63, 106, 9900)-Net in Base 16 — Upper bound on s

There is no (43, 106, 9901)-net in base 16, because

1 times m-reduction [i] would yield (43, 105, 9901)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 710409 964299 027031 620985 828869 086624 552520 400425 598691 658927 238366 289719 258706 636071 169989 240578 807763 176366 486174 364429 829216 > 16¹⁰⁵ [i]