MinT - Best Known (33, 33+86, s)-Nets in Base 16

Best Known (33, 33+86, s)-Nets in Base 16

(33, 33+86, 65)-Net over F₁₆ — Constructive and digital

Digital (33, 119, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 119, 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]

(33, 33+86, 104)-Net in Base 16 — Constructive

(33, 119, 104)-net in base 16, using

1 times m-reduction [i] based on (33, 120, 104)-net in base 16, using
- base change [i] based on digital (9, 96, 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]

(33, 33+86, 193)-Net over F₁₆ — Digital

Digital (33, 119, 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]

(33, 33+86, 2395)-Net in Base 16 — Upper bound on s

There is no (33, 119, 2396)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 196498 938361 693544 695484 391817 338270 071497 196097 146999 141293 833322 170980 659955 097161 657943 061649 764283 064105 715856 780672 328855 516662 926954 425346 > 16¹¹⁹ [i]