MinT - Best Known (7, 7+4, s)-Nets in Base 5

Best Known (7, 7+4, s)-Nets in Base 5

(7, 7+4, 300)-Net over F₅ — Constructive and digital

Digital (7, 11, 300)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹¹, 300, F₅, 4, 4) (dual of [(300, 4), 1189, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(5¹¹, 300, F₅, 3, 4) (dual of [(300, 3), 889, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(5¹¹, 600, F₅, 4) (dual of [600, 589, 5]-code), using
    - base reduction for projective spaces (embedding PG(5,25) in PG(10,5)) [i] based on linear OA(25⁶, 600, F₂₅, 4) (dual of [600, 594, 5]-code), using
      - 1 times truncation [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
        a code by Danev and Olsson [i]

(7, 7+4, 600)-Net over F₅ — Digital

Digital (7, 11, 600)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹¹, 600, F₅, 4, 4) (dual of [(600, 4), 2389, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(5¹¹, 600, F₅, 3, 4) (dual of [(600, 3), 1789, 5]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5¹¹, 600, F₅, 4) (dual of [600, 589, 5]-code), using
    - base reduction for projective spaces (embedding PG(5,25) in PG(10,5)) [i] based on linear OA(25⁶, 600, F₂₅, 4) (dual of [600, 594, 5]-code), using
      - 1 times truncation [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
        a code by Danev and Olsson [i]

(7, 7+4, 2469)-Net in Base 5 — Upper bound on s

There is no (7, 11, 2470)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 846721 > 5¹¹ [i]