MinT - Best Known (65−49, 65, s)-Nets in Base 16

Best Known (65−49, 65, s)-Nets in Base 16

(65−49, 65, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 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]

(65−49, 65, 98)-Net over F₁₆ — Digital

Digital (16, 65, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 65, 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]

(65−49, 65, 1049)-Net in Base 16 — Upper bound on s

There is no (16, 65, 1050)-net in base 16, because

1 times m-reduction [i] would yield (16, 64, 1050)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 117723 400498 851519 702001 038844 968164 488013 379816 574227 611522 910692 156389 143001 > 16⁶⁴ [i]