MinT - Best Known (3, 3+40, s)-Nets in Base 16

Best Known (3, 3+40, s)-Nets in Base 16

(3, 3+40, 38)-Net over F₁₆ — Constructive and digital

Digital (3, 43, 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]

(3, 3+40, 145)-Net in Base 16 — Upper bound on s

There is no (3, 43, 146)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁴³, 146, S₁₆, 40), but
- the linear programming bound shows that MÂ â‰¥ 168 935618 361413 717468 238491 469827 199997 098640 156553 596257 129245 704192 / 27211 192975 580707 > 16⁴³ [i]