MinT - Best Known (129−105, 129, s)-Nets in Base 16

Best Known (129−105, 129, s)-Nets in Base 16

(129−105, 129, 65)-Net over F₁₆ — Constructive and digital

Digital (24, 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]

(129−105, 129, 129)-Net over F₁₆ — Digital

Digital (24, 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]

(129−105, 129, 1212)-Net in Base 16 — Upper bound on s

There is no (24, 129, 1213)-net in base 16, because

1 times m-reduction [i] would yield (24, 128, 1213)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13829 435543 010496 055106 792488 303342 828944 069714 128529 941546 785493 058226 548710 136469 339198 557149 704249 883195 428054 692031 954150 123220 450880 104762 258016 272241 > 16¹²⁸ [i]