MinT - Best Known (117−73, 117, s)-Nets in Base 16

Best Known (117−73, 117, s)-Nets in Base 16

(117−73, 117, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 117, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 117, 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]

(117−73, 117, 226)-Net over F₁₆ — Digital

Digital (44, 117, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 117, 226)-net over F₁₆, using
- net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
    - Drinfeld modules of rank 1 [i]

(117−73, 117, 7200)-Net in Base 16 — Upper bound on s

There is no (44, 117, 7201)-net in base 16, because

1 times m-reduction [i] would yield (44, 116, 7201)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 47 644030 119147 629300 753975 299436 735805 834086 264484 137742 828495 811708 190700 355757 878515 523182 846880 513568 986389 047438 889203 339522 097682 268416 > 16¹¹⁶ [i]