MinT - Best Known (17, 124, s)-Nets in Base 16

Best Known (17, 124, s)-Nets in Base 16

(17, 124, 65)-Net over F₁₆ — Constructive and digital

Digital (17, 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]

(17, 124, 112)-Net over F₁₆ — Digital

Digital (17, 124, 112)-net over F₁₆, using

net from sequence [i] based on digital (17, 111)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 17 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(17, 124, 825)-Net in Base 16 — Upper bound on s

There is no (17, 124, 826)-net in base 16, because

3 times m-reduction [i] would yield (17, 121, 826)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 50 713275 565934 892854 162969 661915 172226 070860 960508 355216 719951 933398 076113 695267 032218 986612 524944 476127 044854 568500 099875 805496 911031 751567 519506 > 16¹²¹ [i]