MinT - Best Known (129−109, 129, s)-Nets in Base 16

Best Known (129−109, 129, s)-Nets in Base 16

(129−109, 129, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 129, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 129, 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]

(129−109, 129, 129)-Net over F₁₆ — Digital

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

t-expansion [i] based on digital (19, 129, 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]

(129−109, 129, 969)-Net in Base 16 — Upper bound on s

There is no (20, 129, 970)-net in base 16, because

1 times m-reduction [i] would yield (20, 128, 970)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13892 011220 453378 006889 650773 762782 062529 933327 517525 189405 724108 686821 239701 176222 010848 273492 221524 178066 318254 071556 955981 973544 311184 082442 010759 978576 > 16¹²⁸ [i]