MinT - Best Known (105−81, 105, s)-Nets in Base 16

Best Known (105−81, 105, s)-Nets in Base 16

(105−81, 105, 65)-Net over F₁₆ — Constructive and digital

Digital (24, 105, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 105, 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]

(105−81, 105, 129)-Net over F₁₆ — Digital

Digital (24, 105, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 105, 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]

(105−81, 105, 1398)-Net in Base 16 — Upper bound on s

There is no (24, 105, 1399)-net in base 16, because

1 times m-reduction [i] would yield (24, 104, 1399)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 172488 574974 768461 005647 123221 489503 237473 818729 469631 350681 772387 531055 026035 254242 128952 021452 536680 045945 739618 100351 380026 > 16¹⁰⁴ [i]