MinT - Best Known (67, 67+48, s)-Nets in Base 16

Best Known (67, 67+48, s)-Nets in Base 16

(67, 67+48, 532)-Net over F₁₆ — Constructive and digital

Digital (67, 115, 532)-net over F₁₆, using

1 times m-reduction [i] based on digital (67, 116, 532)-net over F₁₆, using
- trace code for nets [i] based on digital (9, 58, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(67, 67+48, 1106)-Net over F₁₆ — Digital

Digital (67, 115, 1106)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+48, 384590)-Net in Base 16 — Upper bound on s

There is no (67, 115, 384591)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 977271 056909 546292 948897 971582 795240 748881 025363 639738 295885 027291 278492 257938 075342 562855 247065 472724 692658 261595 369883 711475 818137 106236 > 16¹¹⁵ [i]