MinT - Best Known (65−51, 65, s)-Nets in Base 16

Best Known (65−51, 65, s)-Nets in Base 16

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

Digital (14, 65, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 65, 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]

(65−51, 65, 97)-Net over F₁₆ — Digital

Digital (14, 65, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 65, 97)-net over F₁₆, using
- net from sequence [i] based on digital (13, 96)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 13 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(65−51, 65, 806)-Net in Base 16 — Upper bound on s

There is no (14, 65, 807)-net in base 16, because

1 times m-reduction [i] would yield (14, 64, 807)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 116157 189577 847977 020891 771253 552009 255834 770005 378151 540514 067154 309688 086376 > 16⁶⁴ [i]