MinT - Information on Result #1180416

Information on Result #1180416

Digital (14, 27, 17)-net over F₂, using net defined by OOA based on linear OOA(2²⁷, 17, F₂, 18, 13) (dual of [(17, 18), 279, 14]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2²⁷, 18, F₂, 6, 13) (dual of [(18, 6), 81, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁹, 9, F₂, 6, 6) (dual of [(9, 6), 45, 7]-NRT-code), using
    - appending kth column [i] based on linear OOA(2⁹, 9, F₂, 5, 6) (dual of [(9, 5), 36, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (3, 9, 9)-net over F₂, using
        a shift-net [i]
  2. linear OOA(2¹⁸, 9, F₂, 6, 13) (dual of [(9, 6), 36, 14]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(6;F,40P) [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
      - an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁷, 16, F₂, 3, 13) (dual of [(16, 3), 21, 14]-NRT-code)	[i]		Extracting Embedded OOA
2	Linear OOA(2²⁷, 16, F₂, 4, 13) (dual of [(16, 4), 37, 14]-NRT-code)	[i]
3	Linear OOA(2²⁷, 16, F₂, 5, 13) (dual of [(16, 5), 53, 14]-NRT-code)	[i]
4	Linear OOA(2²⁷, 16, F₂, 6, 13) (dual of [(16, 6), 69, 14]-NRT-code)	[i]