MinT - Best Known (122−73, 122, s)-Nets in Base 16

Best Known (122−73, 122, s)-Nets in Base 16

(122−73, 122, 243)-Net over F₁₆ — Constructive and digital

Digital (49, 122, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 122, 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]

(122−73, 122, 10592)-Net in Base 16 — Upper bound on s

There is no (49, 122, 10593)-net in base 16, because

1 times m-reduction [i] would yield (49, 121, 10593)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 49 976181 687490 030934 710834 377948 009652 514385 652433 199159 130732 857444 000041 186320 161303 530045 892726 605924 179523 019114 617041 895464 393540 339878 550096 > 16¹²¹ [i]