MinT - Best Known (129−83, 129, s)-Nets in Base 16

Best Known (129−83, 129, s)-Nets in Base 16

(129−83, 129, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 129, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 129, 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]

(129−83, 129, 243)-Net over F₁₆ — Digital

Digital (46, 129, 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]

(129−83, 129, 6157)-Net in Base 16 — Upper bound on s

There is no (46, 129, 6158)-net in base 16, because

1 times m-reduction [i] would yield (46, 128, 6158)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13424 348483 445493 519727 761756 627775 963362 970439 702282 638129 321505 019534 115174 866099 690210 261363 671935 558116 989209 851371 550153 387106 483725 300534 590067 007296 > 16¹²⁸ [i]