MinT - Best Known (125−104, 125, s)-Nets in Base 16

Best Known (125−104, 125, s)-Nets in Base 16

(125−104, 125, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 125, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 125, 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]

(125−104, 125, 129)-Net over F₁₆ — Digital

Digital (21, 125, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 125, 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]

(125−104, 125, 1028)-Net in Base 16 — Upper bound on s

There is no (21, 125, 1029)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 299874 612007 740186 166965 308314 805699 466804 848411 342699 069425 004404 012803 756642 721366 806807 878279 092063 412766 826564 329536 847194 048072 647986 561148 050496 > 16¹²⁵ [i]