MinT - Information on Result #1831572

Information on Result #1831572

OOA(4¹⁷³, 4194559, S₄, 2, 17), using (u,Â u+v)-construction based on

OOA(4²⁸, 258, S₄, 2, 8), using
- extracting embedded OOA [i] based on (20, 28, 258)-net in base 4, using
  - trace code for nets [i] based on (6, 14, 129)-net in base 16, using
    - base change [i] based on digital (0, 8, 129)-net over F₁₂₈, using
      - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
        the rational function field F₁₂₈(x) [i]
        Niederreiter sequence [i]
linear OOA(4¹⁴⁵, 4194301, F₄, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁴⁵, 8388602, F₄, 17) (dual of [8388602, 8388457, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁴⁵, large, F₄, 17) (dual of [large, large−145, 18]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

None.

The following results depend on this result:

	Result		This result only	Method
1	OOA(4¹⁷³, 4194559, S₄, 2, 16)	[i]		Strength Reduction for OOAs
2	OOA(4¹⁷⁴, 4194559, S₄, 2, 17)	[i]		OOA Duplication