MinT - Best Known (108−62, 108, s)-Nets in Base 16

Best Known (108−62, 108, s)-Nets in Base 16

(108−62, 108, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 108, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 108, 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]

(108−62, 108, 243)-Net over F₁₆ — Digital

Digital (46, 108, 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]

(108−62, 108, 12952)-Net in Base 16 — Upper bound on s

There is no (46, 108, 12953)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11092 000394 771603 670981 606044 457852 036603 764811 996285 683006 672441 844496 609820 277784 657288 766469 619581 777642 550115 694041 847310 400896 > 16¹⁰⁸ [i]