MinT - Best Known (123−104, 123, s)-Nets in Base 16

Best Known (123−104, 123, s)-Nets in Base 16

(123−104, 123, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 123, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 123, 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]

(123−104, 123, 129)-Net over F₁₆ — Digital

Digital (19, 123, 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]

(123−104, 123, 921)-Net in Base 16 — Upper bound on s

There is no (19, 123, 922)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12869 716448 276981 118201 810247 727791 832495 464671 865087 298380 587501 831432 202383 304262 966202 344379 455631 745780 705461 090413 578097 360186 272990 077094 717336 > 16¹²³ [i]