MinT - Best Known (124−77, 124, s)-Nets in Base 16

Best Known (124−77, 124, s)-Nets in Base 16

(124−77, 124, 225)-Net over F₁₆ — Constructive and digital

Digital (47, 124, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 124, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(124−77, 124, 243)-Net over F₁₆ — Digital

Digital (47, 124, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 124, 243)-net over F₁₆, using
- net from sequence [i] based on digital (46, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 46 and N(F) ≥ 243, using
    - a curve from the manYPoints database [i]

(124−77, 124, 7890)-Net in Base 16 — Upper bound on s

There is no (47, 124, 7891)-net in base 16, because

1 times m-reduction [i] would yield (47, 123, 7891)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12819 364064 184690 398716 025516 354884 475469 619641 638725 621220 934466 360663 843480 049454 133371 194811 393497 235778 801007 534398 677244 632686 141273 678750 444296 > 16¹²³ [i]