MinT - Best Known (61, 61+44, s)-Nets in Base 7

Best Known (61, 61+44, s)-Nets in Base 7

(61, 61+44, 116)-Net over F₇ — Constructive and digital

Digital (61, 105, 116)-net over F₇, using

1 times m-reduction [i] based on digital (61, 106, 116)-net over F₇, using
- trace code for nets [i] based on digital (8, 53, 58)-net over F₄₉, using
  - net from sequence [i] based on digital (8, 57)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(61, 61+44, 319)-Net over F₇ — Digital

Digital (61, 105, 319)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+44, 16283)-Net in Base 7 — Upper bound on s

There is no (61, 105, 16284)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 54401 538164 465696 454729 464363 283587 956254 387605 994886 712747 800361 543183 613675 005882 171977 > 7¹⁰⁵ [i]