MinT - Best Known (117−95, 117, s)-Nets in Base 16

Best Known (117−95, 117, s)-Nets in Base 16

(117−95, 117, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 117, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 117, 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]

(117−95, 117, 129)-Net over F₁₆ — Digital

Digital (22, 117, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 117, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(117−95, 117, 1121)-Net in Base 16 — Upper bound on s

There is no (22, 117, 1122)-net in base 16, because

1 times m-reduction [i] would yield (22, 116, 1122)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 47 936115 133194 508272 548626 520042 803952 071411 336958 335709 237163 049837 156002 052694 870762 845758 834574 451271 365283 540409 118937 884274 703629 091936 > 16¹¹⁶ [i]