MinT - Best Known (7, 7+4, s)-Nets in Base 7

Best Known (7, 7+4, s)-Nets in Base 7

(7, 7+4, 1176)-Net over F₇ — Constructive and digital

Digital (7, 11, 1176)-net over F₇, using

net defined by OOA [i] based on linear OOA(7¹¹, 1176, F₇, 4, 4) (dual of [(1176, 4), 4693, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(7¹¹, 1176, F₇, 3, 4) (dual of [(1176, 3), 3517, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(7¹¹, 2352, F₇, 4) (dual of [2352, 2341, 5]-code), using
    - base reduction for projective spaces (embedding PG(5,49) in PG(10,7)) [i] based on linear OA(49⁶, 2352, F₄₉, 4) (dual of [2352, 2346, 5]-code), using
      - 1 times truncation [i] based on linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 6]-code), using
        a code by Danev and Olsson [i]

(7, 7+4, 2352)-Net over F₇ — Digital

Digital (7, 11, 2352)-net over F₇, using

net defined by OOA [i] based on linear OOA(7¹¹, 2352, F₇, 4, 4) (dual of [(2352, 4), 9397, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(7¹¹, 2352, F₇, 3, 4) (dual of [(2352, 3), 7045, 5]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7¹¹, 2352, F₇, 4) (dual of [2352, 2341, 5]-code), using
    - base reduction for projective spaces (embedding PG(5,49) in PG(10,7)) [i] based on linear OA(49⁶, 2352, F₄₉, 4) (dual of [2352, 2346, 5]-code), using
      - 1 times truncation [i] based on linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 6]-code), using
        a code by Danev and Olsson [i]

(7, 7+4, 10480)-Net in Base 7 — Upper bound on s

There is no (7, 11, 10481)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1977 638929 > 7¹¹ [i]