MinT - Information on Result #1185888

Information on Result #1185888

Digital (64, 71, 2801240)-net over F₄, using net defined by OOA based on linear OOA(4⁷¹, 2801240, F₄, 9, 7) (dual of [(2801240, 9), 25211089, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(4⁷¹, 2801241, F₄, 3, 7) (dual of [(2801241, 3), 8403652, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(4¹⁰, 5040, F₄, 3, 3) (dual of [(5040, 3), 15110, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(4¹⁰, 5040, F₄, 2, 3) (dual of [(5040, 2), 10070, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4¹⁰, 5040, F₄, 3) (dual of [5040, 5030, 4]-code or 5040-cap in PG(9,4)), using
        product of projective cap with cap in AG(4,Â 4) [i] based on linear OA(4⁶, 126, F₄, 3) (dual of [126, 120, 4]-code or 126-cap in PG(5,4)), using
        the Glynn cap [i]
  2. linear OOA(4⁶¹, 2796201, F₄, 3, 7) (dual of [(2796201, 3), 8388542, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(4⁶¹, large, F₄, 7) (dual of [large, large−61, 8]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (216, 230, 6396353)-net over F₄	[i]	(u,Â u+v)-Construction for Nets
2	Digital (217, 231, 7594724)-net over F₄	[i]
3	Digital (227, 242, 6396353)-net over F₄	[i]
4	Digital (228, 243, 7594724)-net over F₄	[i]