MinT - Best Known (49, 49+71, s)-Nets in Base 16

Best Known (49, 49+71, s)-Nets in Base 16

(49, 49+71, 243)-Net over F₁₆ — Constructive and digital

Digital (49, 120, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 120, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(49, 49+71, 11493)-Net in Base 16 — Upper bound on s

There is no (49, 120, 11494)-net in base 16, because

1 times m-reduction [i] would yield (49, 119, 11494)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 195428 757896 262101 723246 335252 362601 206709 980602 340829 357110 876102 623340 699199 664059 138715 085980 663246 905928 552807 508189 621258 598261 085078 736226 > 16¹¹⁹ [i]