MinT - Best Known (42, 124, s)-Nets in Base 16

Best Known (42, 124, s)-Nets in Base 16

(42, 124, 225)-Net over F₁₆ — Constructive and digital

Digital (42, 124, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 124, 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]

(42, 124, 4693)-Net in Base 16 — Upper bound on s

There is no (42, 124, 4694)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 206302 461840 995893 417674 769132 650282 945938 846146 560831 727581 433000 983049 623895 006632 114311 273651 006800 771052 808072 640075 487999 274985 751794 134218 532436 > 16¹²⁴ [i]