MinT - Best Known (47, 47+61, s)-Nets in Base 16

Best Known (47, 47+61, s)-Nets in Base 16

(47, 47+61, 225)-Net over F₁₆ — Constructive and digital

Digital (47, 108, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 108, 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]

(47, 47+61, 243)-Net over F₁₆ — Digital

Digital (47, 108, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 108, 243)-net over F₁₆, using
- net from sequence [i] based on digital (46, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 46 and N(F) ≥ 243, using
    - a curve from the manYPoints database [i]

(47, 47+61, 15810)-Net in Base 16 — Upper bound on s

There is no (47, 108, 15811)-net in base 16, because

1 times m-reduction [i] would yield (47, 107, 15811)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 694 134781 777974 042655 915658 666311 057160 522640 135573 365057 295727 399272 407067 948541 161280 547426 678745 741690 547753 083932 698679 986576 > 16¹⁰⁷ [i]