MinT - Best Known (127−59, 127, s)-Nets in Base 16

Best Known (127−59, 127, s)-Nets in Base 16

(127−59, 127, 522)-Net over F₁₆ — Constructive and digital

Digital (68, 127, 522)-net over F₁₆, using

1 times m-reduction [i] based on digital (68, 128, 522)-net over F₁₆, using
- trace code for nets [i] based on digital (4, 64, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(127−59, 127, 649)-Net over F₁₆ — Digital

Digital (68, 127, 649)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−59, 127, 132639)-Net in Base 16 — Upper bound on s

There is no (68, 127, 132640)-net in base 16, because

1 times m-reduction [i] would yield (68, 126, 132640)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 52 381912 828961 874994 250513 288401 035908 473073 655064 569162 735654 219495 050988 609057 953475 452868 609721 572114 743257 912543 643012 897261 555677 667231 618102 259151 > 16¹²⁶ [i]