MinT - Best Known (67, 67+54, s)-Nets in Base 16

Best Known (67, 67+54, s)-Nets in Base 16

(67, 67+54, 526)-Net over F₁₆ — Constructive and digital

Digital (67, 121, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (67, 122, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 61, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(67, 67+54, 785)-Net over F₁₆ — Digital

Digital (67, 121, 785)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+54, 181351)-Net in Base 16 — Upper bound on s

There is no (67, 121, 181352)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 49 950693 968960 346251 162749 296388 709957 316015 245260 822523 390250 944714 126117 513432 501255 587537 005988 299352 655947 736471 886898 433583 279329 966464 478236 > 16¹²¹ [i]