MinT - Best Known (21, 114, s)-Nets in Base 16

Best Known (21, 114, s)-Nets in Base 16

(21, 114, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 114, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 114, 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]

(21, 114, 129)-Net over F₁₆ — Digital

Digital (21, 114, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 114, 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]

(21, 114, 1063)-Net in Base 16 — Upper bound on s

There is no (21, 114, 1064)-net in base 16, because

1 times m-reduction [i] would yield (21, 113, 1064)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11765 214488 752236 984615 413802 087707 174441 922952 257138 522762 489343 126733 068826 463049 401872 216610 290874 715955 936562 630097 926422 974719 473536 > 16¹¹³ [i]