MinT - Best Known (129−122, 129, s)-Nets in Base 16

Best Known (129−122, 129, s)-Nets in Base 16

(129−122, 129, 65)-Net over F₁₆ — Constructive and digital

Digital (7, 129, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 129, 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]

(129−122, 129, 119)-Net in Base 16 — Upper bound on s

There is no (7, 129, 120)-net in base 16, because

18 times m-reduction [i] would yield (7, 111, 120)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16¹¹¹, 120, S₁₆, 104), but
  - the linear programming bound shows that MÂ â‰¥ 92086 954283 537596 660104 192126 770459 664696 363604 028357 116797 528075 544556 954927 352946 662893 970276 794850 999821 883009 523266 007059 187150 407449 182208 / 1974 452051 > 16¹¹¹ [i]