MinT - Best Known (29, 29+91, s)-Nets in Base 16

Best Known (29, 29+91, s)-Nets in Base 16

(29, 29+91, 65)-Net over F₁₆ — Constructive and digital

Digital (29, 120, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 120, 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]

(29, 29+91, 76)-Net in Base 16 — Constructive

(29, 120, 76)-net in base 16, using

base change [i] based on digital (5, 96, 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]

(29, 29+91, 161)-Net over F₁₆ — Digital

Digital (29, 120, 161)-net over F₁₆, using

net from sequence [i] based on digital (29, 160)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 29 and N(F) ≥ 161, using
  - a curve from the manYPoints database [i]

(29, 29+91, 1771)-Net in Base 16 — Upper bound on s

There is no (29, 120, 1772)-net in base 16, because

1 times m-reduction [i] would yield (29, 119, 1772)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 199537 972227 701848 203854 884589 815888 873685 797557 528292 844359 476205 737849 233210 014074 124779 484388 210247 395611 971846 615140 088561 468102 683410 644976 > 16¹¹⁹ [i]