MinT - Best Known (124−108, 124, s)-Nets in Base 16

Best Known (124−108, 124, s)-Nets in Base 16

(124−108, 124, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 124, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 124, 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]

(124−108, 124, 98)-Net over F₁₆ — Digital

Digital (16, 124, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 124, 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]

(124−108, 124, 779)-Net in Base 16 — Upper bound on s

There is no (16, 124, 780)-net in base 16, because

8 times m-reduction [i] would yield (16, 116, 780)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 48 003585 677147 096241 378194 527010 459665 811218 295288 638809 543921 178116 838708 610033 793946 458866 399917 141439 403954 638714 025846 327459 605652 219376 > 16¹¹⁶ [i]