MinT - Information on Result #897163

Information on Result #897163

Linear OOA(8¹⁵³, 399, F₈, 2, 52) (dual of [(399, 2), 645, 53]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8³⁵, 45, F₈, 2, 26) (dual of [(45, 2), 55, 27]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,63P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
  - an explicitly constructive algebraic function field [i]
linear OOA(8¹¹⁸, 354, F₈, 2, 52) (dual of [(354, 2), 590, 53]-NRT-code), using
- extracting embedded OOA [i] based on digital (66, 118, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 59, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁵³, 199, F₈, 3, 52) (dual of [(199, 3), 444, 53]-NRT-code)	[i]		OOA Folding