MinT - Best Known (126−79, 126, s)-Nets in Base 16

Best Known (126−79, 126, s)-Nets in Base 16

(126−79, 126, 225)-Net over F₁₆ — Constructive and digital

Digital (47, 126, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 126, 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]

(126−79, 126, 243)-Net over F₁₆ — Digital

Digital (47, 126, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 126, 243)-net over F₁₆, using
- net from sequence [i] based on digital (46, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 46 and N(F) ≥ 243, using
    - a curve from the manYPoints database [i]

(126−79, 126, 7403)-Net in Base 16 — Upper bound on s

There is no (47, 126, 7404)-net in base 16, because

1 times m-reduction [i] would yield (47, 125, 7404)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 284497 291400 632810 218354 433894 910552 336381 404026 751721 363648 699269 220684 599735 948544 521758 483112 159993 477430 684187 690918 750900 688599 910869 060367 995466 > 16¹²⁵ [i]