MinT - Best Known (15, 15+34, s)-Nets in Base 16

Best Known (15, 15+34, s)-Nets in Base 16

(15, 15+34, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 49, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 49, 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]

(15, 15+34, 76)-Net in Base 16 — Constructive

(15, 49, 76)-net in base 16, using

1 times m-reduction [i] based on (15, 50, 76)-net in base 16, using
- base change [i] based on digital (5, 40, 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]

(15, 15+34, 98)-Net over F₁₆ — Digital

Digital (15, 49, 98)-net over F₁₆, using

net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(15, 15+34, 1405)-Net in Base 16 — Upper bound on s

There is no (15, 49, 1406)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 101381 396439 786099 493335 892920 326106 681147 122438 427855 806131 > 16⁴⁹ [i]