MinT - Best Known (109−48, 109, s)-Nets in Base 16

Best Known (109−48, 109, s)-Nets in Base 16

(109−48, 109, 526)-Net over F₁₆ — Constructive and digital

Digital (61, 109, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (61, 110, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 55, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(109−48, 109, 783)-Net over F₁₆ — Digital

Digital (61, 109, 783)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−48, 109, 192288)-Net in Base 16 — Upper bound on s

There is no (61, 109, 192289)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 177460 287363 532908 851973 575434 633316 631973 343878 203312 623720 837205 687923 458554 373951 555026 857295 451913 972742 587286 507285 428716 593916 > 16¹⁰⁹ [i]