MinT - Best Known (124−104, 124, s)-Nets in Base 16

Best Known (124−104, 124, s)-Nets in Base 16

(124−104, 124, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 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]

(124−104, 124, 129)-Net over F₁₆ — Digital

Digital (20, 124, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 124, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(124−104, 124, 973)-Net in Base 16 — Upper bound on s

There is no (20, 124, 974)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 205299 185729 018248 987274 619279 689959 676479 235179 846687 733671 217443 775456 969298 728283 758940 479018 937237 464222 493712 972907 251244 365462 511513 854897 376596 > 16¹²⁴ [i]