MinT - Information on Result #1218797

Information on Result #1218797

Digital (64, 75, 3388080)-net over F₁₆, using (u,Â u+v)-construction based on

digital (8, 13, 32640)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16¹³, 32640, F₁₆, 5, 5) (dual of [(32640, 5), 163187, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(16¹³, 65281, F₁₆, 5) (dual of [65281, 65268, 6]-code), using
    - base reduction for projective spaces (embedding PG(6,256) in PG(12,16)) [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
      - a code by Danev and Olsson [i]
digital (51, 62, 3355440)-net over F₁₆, using
- trace code for nets [i] based on digital (20, 31, 1677720)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256³¹, 1677720, F₂₅₆, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(256³¹, 8388601, F₂₅₆, 11) (dual of [8388601, 8388570, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(256³¹, large, F₂₅₆, 11) (dual of [large, large−31, 12]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	(89, 100, 3388080)-net in base 8	[i]		Base Change