MinT - Best Known (110−67, 110, s)-Nets in Base 16

Best Known (110−67, 110, s)-Nets in Base 16

(110−67, 110, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 110, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 110, 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]

(110−67, 110, 226)-Net over F₁₆ — Digital

Digital (43, 110, 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]

(110−67, 110, 8309)-Net in Base 16 — Upper bound on s

There is no (43, 110, 8310)-net in base 16, because

1 times m-reduction [i] would yield (43, 109, 8310)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 178031 384441 291909 037667 731571 253479 021613 854303 685638 059914 853015 361562 564990 300380 609298 446345 976189 098902 298558 926444 028434 597451 > 16¹⁰⁹ [i]