MinT - Best Known (66−51, 66, s)-Nets in Base 16

Best Known (66−51, 66, s)-Nets in Base 16

(66−51, 66, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 66, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 66, 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]

(66−51, 66, 98)-Net over F₁₆ — Digital

Digital (15, 66, 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]

(66−51, 66, 903)-Net in Base 16 — Upper bound on s

There is no (15, 66, 904)-net in base 16, because

1 times m-reduction [i] would yield (15, 65, 904)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 897369 719250 953662 454267 821179 547817 502113 201119 865930 027300 268824 508330 623376 > 16⁶⁵ [i]