MinT - Best Known (109−87, 109, s)-Nets in Base 16

Best Known (109−87, 109, s)-Nets in Base 16

(109−87, 109, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 109, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 109, 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]

(109−87, 109, 129)-Net over F₁₆ — Digital

Digital (22, 109, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 109, 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]

(109−87, 109, 1166)-Net in Base 16 — Upper bound on s

There is no (22, 109, 1167)-net in base 16, because

1 times m-reduction [i] would yield (22, 108, 1167)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11247 175191 299950 736114 763962 120442 214357 568946 305492 880667 158612 728534 698278 383792 485499 137820 108263 004628 113572 785221 283544 317616 > 16¹⁰⁸ [i]