MinT - Best Known (96−73, 96, s)-Nets in Base 16

Best Known (96−73, 96, s)-Nets in Base 16

(96−73, 96, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 96, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 96, 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]

(96−73, 96, 129)-Net over F₁₆ — Digital

Digital (23, 96, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 96, 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]

(96−73, 96, 1412)-Net in Base 16 — Upper bound on s

There is no (23, 96, 1413)-net in base 16, because

1 times m-reduction [i] would yield (23, 95, 1413)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 464750 149449 004539 759135 530735 657749 188485 052376 308754 575679 514845 750519 800715 285278 682616 210648 468760 888935 765396 > 16⁹⁵ [i]