MinT - Best Known (18, 105, s)-Nets in Base 16

Best Known (18, 105, s)-Nets in Base 16

(18, 105, 65)-Net over F₁₆ — Constructive and digital

Digital (18, 105, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 105, 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]

(18, 105, 113)-Net over F₁₆ — Digital

Digital (18, 105, 113)-net over F₁₆, using

net from sequence [i] based on digital (18, 112)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 18 and N(F) ≥ 113, using
  - a curve from the manYPoints database [i]

(18, 105, 896)-Net in Base 16 — Upper bound on s

There is no (18, 105, 897)-net in base 16, because

1 times m-reduction [i] would yield (18, 104, 897)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 177072 251451 392268 163377 746701 843598 770683 805157 126605 061589 324051 990635 161704 445697 724399 150439 499516 846892 852662 430321 337216 > 16¹⁰⁴ [i]