MinT - Information on Result #1838621

Information on Result #1838621

OOA(128⁴⁹, 2097536, S₁₂₈, 4, 12), using (u,Â u+v)-construction based on

OOA(128¹⁰, 386, S₁₂₈, 4, 6), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128³, 129, F₁₂₈, 4, 3) (dual of [(129, 4), 513, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(4;513,128) [i]
  2. OOA(128⁷, 257, S₁₂₈, 4, 6), using
    - extracting embedded OOA [i] based on (1, 7, 257)-net in base 128, using
      - 1 times m-reduction [i] based on (1, 8, 257)-net in base 128, using
        base change [i] based on digital (0, 7, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
OOA(128³⁹, 2097150, S₁₂₈, 4, 12), using
- OOA 4-folding [i] based on OA(128³⁹, 8388600, S₁₂₈, 12), using
  - discarding factors based on OA(128³⁹, large, S₁₂₈, 12), using
    - discarding parts of the base [i] based on linear OA(256³⁴, large, F₂₅₆, 12) (dual of [large, large−34, 13]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

None.

The following results depend on this result:

	Result		This result only	Method
1	OOA(128⁶⁸, 4195072, S₁₂₈, 4, 12)	[i]		(u,Â u+v)-Construction for OOAs