MinT - Best Known (64, 64+53, s)-Nets in Base 16

Best Known (64, 64+53, s)-Nets in Base 16

(64, 64+53, 524)-Net over F₁₆ — Constructive and digital

Digital (64, 117, 524)-net over F₁₆, using

1 times m-reduction [i] based on digital (64, 118, 524)-net over F₁₆, using
- trace code for nets [i] based on digital (5, 59, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(64, 64+53, 701)-Net over F₁₆ — Digital

Digital (64, 117, 701)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+53, 165726)-Net in Base 16 — Upper bound on s

There is no (64, 117, 165727)-net in base 16, because

1 times m-reduction [i] would yield (64, 116, 165727)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 47 637439 465560 658718 808117 351905 067879 945349 037278 805257 258203 873722 618004 350019 159058 737498 306099 928466 542660 111655 577373 234533 238645 937281 > 16¹¹⁶ [i]