MinT - Best Known (53, 77, s)-Nets in Base 7

Best Known (53, 77, s)-Nets in Base 7

(53, 77, 204)-Net over F₇ — Constructive and digital

Digital (53, 77, 204)-net over F₇, using

1 times m-reduction [i] based on digital (53, 78, 204)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 26, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 13, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]
  2. digital (27, 52, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 26, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(53, 77, 1072)-Net over F₇ — Digital

Digital (53, 77, 1072)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 77, 233296)-Net in Base 7 — Upper bound on s

There is no (53, 77, 233297)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 118183 113127 802595 427947 904446 814105 129191 815104 451353 294224 741793 > 7⁷⁷ [i]