MinT - Best Known (41, 41+77, s)-Nets in Base 16

Best Known (41, 41+77, s)-Nets in Base 16

(41, 41+77, 225)-Net over F₁₆ — Constructive and digital

Digital (41, 118, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 118, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(41, 41+77, 5085)-Net in Base 16 — Upper bound on s

There is no (41, 118, 5086)-net in base 16, because

1 times m-reduction [i] would yield (41, 117, 5086)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 764 342654 731668 324143 083230 450435 096078 608232 403222 213892 014396 330952 329473 628479 084674 896110 427740 521242 318707 815428 117371 644065 547618 830696 > 16¹¹⁷ [i]