MinT - Best Known (15, 42, s)-Nets in Base 16

Best Known (15, 42, s)-Nets in Base 16

(15, 42, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 42, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 42, 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, 42, 80)-Net in Base 16 — Constructive

(15, 42, 80)-net in base 16, using

base change [i] based on digital (1, 28, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(15, 42, 98)-Net over F₁₆ — Digital

Digital (15, 42, 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, 42, 2364)-Net in Base 16 — Upper bound on s

There is no (15, 42, 2365)-net in base 16, because

1 times m-reduction [i] would yield (15, 41, 2365)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 23 499953 450258 525241 828060 800808 947809 557879 302176 > 16⁴¹ [i]