MinT - Best Known (106−60, 106, s)-Nets in Base 16

Best Known (106−60, 106, s)-Nets in Base 16

(106−60, 106, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 106, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 106, 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]

(106−60, 106, 243)-Net over F₁₆ — Digital

Digital (46, 106, 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]

(106−60, 106, 14413)-Net in Base 16 — Upper bound on s

There is no (46, 106, 14414)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 43 402504 788737 387544 273605 386574 504582 521591 957954 194485 525345 695345 725641 936942 146965 465025 887594 592912 071027 136912 730370 038176 > 16¹⁰⁶ [i]