MinT - Best Known (90−75, 90, s)-Nets in Base 16

Best Known (90−75, 90, s)-Nets in Base 16

(90−75, 90, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 90, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 90, 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]

(90−75, 90, 98)-Net over F₁₆ — Digital

Digital (15, 90, 98)-net over F₁₆, using

net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(90−75, 90, 749)-Net in Base 16 — Upper bound on s

There is no (15, 90, 750)-net in base 16, because

1 times m-reduction [i] would yield (15, 89, 750)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 152661 007581 292547 861849 439077 738206 705936 313610 279498 703516 470670 397597 138141 784506 820773 179345 781023 953751 > 16⁸⁹ [i]