MinT - Best Known (66, 66+29, s)-Nets in Base 7

Best Known (66, 66+29, s)-Nets in Base 7

(66, 66+29, 208)-Net over F₇ — Constructive and digital

Digital (66, 95, 208)-net over F₇, using

7¹ times duplication [i] based on digital (65, 94, 208)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (18, 32, 104)-net over F₇, using
    - trace code for nets [i] based on digital (2, 16, 52)-net over F₄₉, using
      - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
        Niederreiter sequence [i]
  2. digital (33, 62, 104)-net over F₇, using
    - trace code for nets [i] based on digital (2, 31, 52)-net over F₄₉, using
      - net from sequence [i] based on digital (2, 51)-sequence over F₄₉ (see above)

(66, 66+29, 1401)-Net over F₇ — Digital

Digital (66, 95, 1401)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+29, 475913)-Net in Base 7 — Upper bound on s

There is no (66, 95, 475914)-net in base 7, because

1 times m-reduction [i] would yield (66, 94, 475914)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 27 492911 408488 717656 601833 940756 106109 201639 207957 830619 546619 539254 280984 231181 > 7⁹⁴ [i]