MinT - Best Known (34, 34+91, s)-Nets in Base 16

Best Known (34, 34+91, s)-Nets in Base 16

(34, 34+91, 65)-Net over F₁₆ — Constructive and digital

Digital (34, 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]

(34, 34+91, 104)-Net in Base 16 — Constructive

(34, 125, 104)-net in base 16, using

base change [i] based on digital (9, 100, 104)-net over F₃₂, using
- net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(34, 34+91, 193)-Net over F₁₆ — Digital

Digital (34, 125, 193)-net over F₁₆, using

t-expansion [i] based on digital (33, 125, 193)-net over F₁₆, using
- net from sequence [i] based on digital (33, 192)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 33 and N(F) ≥ 193, using
    - a curve from the manYPoints database [i]

(34, 34+91, 2419)-Net in Base 16 — Upper bound on s

There is no (34, 125, 2420)-net in base 16, because

1 times m-reduction [i] would yield (34, 124, 2420)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 208132 210413 675627 826062 171630 747428 513474 748280 465696 823508 601878 400076 486112 058307 752731 381972 062713 553530 903194 981559 299458 804414 416365 594207 307876 > 16¹²⁴ [i]