MinT - Best Known (125−95, 125, s)-Nets in Base 16

Best Known (125−95, 125, s)-Nets in Base 16

(125−95, 125, 65)-Net over F₁₆ — Constructive and digital

Digital (30, 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]

(125−95, 125, 76)-Net in Base 16 — Constructive

(30, 125, 76)-net in base 16, using

base change [i] based on digital (5, 100, 76)-net over F₃₂, using
- net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(125−95, 125, 162)-Net over F₁₆ — Digital

Digital (30, 125, 162)-net over F₁₆, using

net from sequence [i] based on digital (30, 161)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 30 and N(F) ≥ 162, using
  - a curve from the manYPoints database [i]

(125−95, 125, 1814)-Net in Base 16 — Upper bound on s

There is no (30, 125, 1815)-net in base 16, because

1 times m-reduction [i] would yield (30, 124, 1815)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 209708 106311 076429 190258 347509 765174 579457 663598 589160 430522 451628 399819 100605 268935 128190 936969 731492 896448 762467 546643 073541 413833 298791 227110 856576 > 16¹²⁴ [i]