MinT - Best Known (81−34, 81, s)-Nets in Base 16

Best Known (81−34, 81, s)-Nets in Base 16

(81−34, 81, 526)-Net over F₁₆ — Constructive and digital

Digital (47, 81, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (47, 82, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 41, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(81−34, 81, 809)-Net over F₁₆ — Digital

Digital (47, 81, 809)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(81−34, 81, 261286)-Net in Base 16 — Upper bound on s

There is no (47, 81, 261287)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 34 177760 229834 966359 264138 368302 274864 215594 847970 961741 265441 123933 947280 321997 745778 776261 026236 > 16⁸¹ [i]