MinT - Best Known (52, 52+61, s)-Nets in Base 16

Best Known (52, 52+61, s)-Nets in Base 16

(52, 52+61, 243)-Net over F₁₆ — Constructive and digital

Digital (52, 113, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 113, 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]

(52, 52+61, 271)-Net over F₁₆ — Digital

Digital (52, 113, 271)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+61, 25106)-Net in Base 16 — Upper bound on s

There is no (52, 113, 25107)-net in base 16, because

1 times m-reduction [i] would yield (52, 112, 25107)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 726 909816 955453 592315 619045 088451 976986 812940 790029 917672 774432 243466 634444 055882 467652 983470 388064 716763 046331 343734 756191 350793 051776 > 16¹¹² [i]