MinT - Best Known (50−45, 50, s)-Nets in Base 16

Best Known (50−45, 50, s)-Nets in Base 16

(50−45, 50, 49)-Net over F₁₆ — Constructive and digital

Digital (5, 50, 49)-net over F₁₆, using

net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
  - a function field by SÃ©mirat [i]

(50−45, 50, 246)-Net in Base 16 — Upper bound on s

There is no (5, 50, 247)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁵⁰, 247, S₁₆, 45), but
- the linear programming bound shows that MÂ â‰¥ 59 934124 184467 564006 756424 631098 016543 059570 592262 909014 851092 411426 062246 282183 831976 586471 981807 828992 / 36 688815 343437 188002 533756 330859 541800 297327 > 16⁵⁰ [i]