MinT - Information on Result #1841330

Information on Result #1841330

OOA(64³⁰, 2812585, S₆₄, 9, 7), using OOA stacking with additional row 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.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	(23, 30, 2812585)-net in base 64	[i]		Net Defined by OOA