MinT - Information on Result #1568453

Information on Result #1568453

Linear OOA(256¹⁷, 546, F₂₅₆, 3, 11) (dual of [(546, 3), 1621, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256⁵, 257, F₂₅₆, 3, 5) (dual of [(257, 3), 766, 6]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;766,256) [i]
linear OOA(256¹², 289, F₂₅₆, 3, 11) (dual of [(289, 3), 855, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,855P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
  - sharp bound on the number of rational points on curves with genus 1 [i]

Mode: Linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(256¹⁷, 546, F₂₅₆, 4, 11) (dual of [(546, 4), 2167, 12]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256¹⁷, 546, F₂₅₆, 5, 11) (dual of [(546, 5), 2713, 12]-NRT-code)	[i]
3	Linear OOA(256¹⁷, 546, F₂₅₆, 6, 11) (dual of [(546, 6), 3259, 12]-NRT-code)	[i]
4	Digital (6, 17, 546)-net over F₂₅₆	[i]