MinT - Information on Result #1841331

Information on Result #1841331

(23, 30, 2812585)-net in base 64, using net defined by OOA based on OOA(64³⁰, 2812585, S₆₄, 9, 7), using

OOA stacking with additional row [i] based on OOA(64³⁰, 2812586, S₆₄, 3, 7), using
- (u,Â u+v)-construction [i] based on
  1. OOA(64⁵, 16385, S₆₄, 3, 3), using
    - appending kth column [i] based on OOA(64⁵, 16385, S₆₄, 2, 3), using
      - discarding parts of the base [i] based on linear OOA(128⁴, 16385, F₁₂₈, 2, 3) (dual of [(16385, 2), 32766, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁴, 16385, F₁₂₈, 3) (dual of [16385, 16381, 4]-code or 16385-cap in PG(3,128)), using
        ovoid in PG(3,Â 128) [i]
  2. linear OOA(64²⁵, 2796201, F₆₄, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64²⁵, large, F₆₄, 7) (dual of [large, large−25, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]

Mode: Constructive.

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		This result only	Method
1	(29, 36, 2812585)-net in base 32	[i]		Base Change