MinT - Best Known (63−47, 63, s)-Nets in Base 16

Best Known (63−47, 63, s)-Nets in Base 16

(63−47, 63, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 63, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 63, 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]

(63−47, 63, 98)-Net over F₁₆ — Digital

Digital (16, 63, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 63, 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]

(63−47, 63, 1094)-Net in Base 16 — Upper bound on s

There is no (16, 63, 1095)-net in base 16, because

1 times m-reduction [i] would yield (16, 62, 1095)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 454 450340 782279 041058 152518 117152 018651 080455 293034 172564 380842 157120 315776 > 16⁶² [i]