MinT - Best Known (125−103, 125, s)-Nets in Base 16

Best Known (125−103, 125, s)-Nets in Base 16

(125−103, 125, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 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]

(125−103, 125, 129)-Net over F₁₆ — Digital

Digital (22, 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]

(125−103, 125, 1092)-Net in Base 16 — Upper bound on s

There is no (22, 125, 1093)-net in base 16, because

1 times m-reduction [i] would yield (22, 124, 1093)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 211016 920320 503033 067035 036619 477801 761194 778235 614003 294806 074577 819169 152495 630103 389230 141961 068143 977541 282306 444740 177190 579424 940006 249511 594896 > 16¹²⁴ [i]