MinT - Information on Result #895122

Information on Result #895122

Linear OOA(3¹⁷⁰, 4194369, F₃, 2, 15) (dual of [(4194369, 2), 8388568, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁰, 68, F₃, 2, 7) (dual of [(68, 2), 116, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁶, 56, F₃, 2, 3) (dual of [(56, 2), 106, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
      - the Hill cap [i]
  2. linear OOA(3¹⁴, 34, F₃, 2, 7) (dual of [(34, 2), 54, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 14, 34)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3¹⁵⁰, 4194301, F₃, 2, 15) (dual of [(4194301, 2), 8388452, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁵⁰, 8388602, F₃, 15) (dual of [8388602, 8388452, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁵⁰, large, F₃, 15) (dual of [large, large−150, 16]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁷⁰, 2097184, F₃, 4, 15) (dual of [(2097184, 4), 8388566, 16]-NRT-code)	[i]		OOA Folding