MinT - Information on Result #3226412

Information on Result #3226412

Digital (51, 56, large)-net over F₈, using t-expansion based on digital (50, 56, large)-net over F₈, using

trace code for nets [i] based on digital (22, 28, 5592401)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64²⁸, 5592401, F₆₄, 9, 6) (dual of [(5592401, 9), 50331581, 7]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(64²⁸, 5592402, F₆₄, 3, 6) (dual of [(5592402, 3), 16777178, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(64⁷, large, F₆₄, 3, 3), using
        appending kth column [i] based on linear OOA(64⁷, large, F₆₄, 2, 3), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(64⁷, large, F₆₄, 3) (dual of [large, large−7, 4]-code), using
        product of projective cap with 64²-ovoid cap in AG(3,Â 64) [i] based on linear OA(64⁴, 4097, F₆₄, 3) (dual of [4097, 4093, 4]-code or 4097-cap in PG(3,64)), using
        ovoid in PG(3,Â 64) [i]
      2. linear OOA(64²¹, 2796201, F₆₄, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
        OOA 3-folding [i] based on linear OA(64²¹, large, F₆₄, 6) (dual of [large, large−21, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (52, 57, large)-net over F₈	[i]		Net Duplication
2	Digital (53, 58, large)-net over F₈	[i]
3	Digital (54, 59, large)-net over F₈	[i]