MinT - Information on Result #1021830

Information on Result #1021830

Linear OOA(7¹⁰⁴, 45, F₇, 3, 62) (dual of [(45, 3), 31, 63]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7¹³, 9, F₇, 3, 12) (dual of [(9, 3), 14, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹³, 13, F₇, 3, 12) (dual of [(13, 3), 26, 13]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 13, 13)-net over F₇, using
    - a shift-net [i]
linear OOA(7¹⁶, 9, F₇, 3, 15) (dual of [(9, 3), 11, 16]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 16, 9)-net over F₇, using
  - net from sequence [i] based on digital (1, 8)-sequence over F₇, using
    - Niederreiter sequence [i]
linear OOA(7²¹, 9, F₇, 3, 20) (dual of [(9, 3), 6, 21]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 21, 9)-net over F₇, using
  - net from sequence [i] based on digital (1, 8)-sequence over F₇ (see above)
linear OOA(7²⁷, 9, F₇, 3, 27) (dual of [(9, 3), 0, 28]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]
linear OOA(7²⁷, 9, F₇, 3, 27) (dual of [(9, 3), 0, 28]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7¹⁰², 44, F₇, 3, 60) (dual of [(44, 3), 30, 61]-NRT-code)	[i]		Truncation for OOAs