MinT - Best Known (129−58, 129, s)-Nets in Base 16

Best Known (129−58, 129, s)-Nets in Base 16

(129−58, 129, 526)-Net over F₁₆ — Constructive and digital

Digital (71, 129, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (71, 130, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 65, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(129−58, 129, 791)-Net over F₁₆ — Digital

Digital (71, 129, 791)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−58, 129, 176705)-Net in Base 16 — Upper bound on s

There is no (71, 129, 176706)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 214551 143911 915609 914028 611289 712036 436587 438100 198213 871435 486865 977288 719000 562188 924151 307029 530108 432438 862666 422384 219212 082961 979643 213866 283525 028336 > 16¹²⁹ [i]