MinT - Best Known (119−99, 119, s)-Nets in Base 16

Best Known (119−99, 119, s)-Nets in Base 16

(119−99, 119, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 119, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 119, 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]

(119−99, 119, 129)-Net over F₁₆ — Digital

Digital (20, 119, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 119, 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]

(119−99, 119, 984)-Net in Base 16 — Upper bound on s

There is no (20, 119, 985)-net in base 16, because

1 times m-reduction [i] would yield (20, 118, 985)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12590 237321 426403 297103 022835 943676 301871 072457 764104 594230 249507 898924 594963 833707 419642 916792 107281 640093 994219 592584 965751 126021 533403 176976 > 16¹¹⁸ [i]