MinT - Best Known (30−27, 30, s)-Nets in Base 16

Best Known (30−27, 30, s)-Nets in Base 16

(30−27, 30, 38)-Net over F₁₆ — Constructive and digital

Digital (3, 30, 38)-net over F₁₆, using

net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
  - a function field by SÃ©mirat [i]

(30−27, 30, 170)-Net in Base 16 — Upper bound on s

There is no (3, 30, 171)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16³⁰, 171, S₁₆, 27), but
- the linear programming bound shows that MÂ â‰¥ 1 692948 843458 152892 108119 879540 787513 074799 322665 724661 465088 / 1 215785 540371 935606 103343 > 16³⁰ [i]