MinT - Information on Result #1616179

Information on Result #1616179

Linear OOA(256⁴⁰, 610, F₂₅₆, 4, 25) (dual of [(610, 4), 2400, 26]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹³, 289, F₂₅₆, 4, 12) (dual of [(289, 4), 1143, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,1143P) [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]
linear OOA(256²⁷, 321, F₂₅₆, 4, 25) (dual of [(321, 4), 1257, 26]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,1258P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
  - sharp bound on the number of rational points on curves with genus 2 [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(256⁴⁰, 610, F₂₅₆, 5, 25) (dual of [(610, 5), 3010, 26]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256⁴⁰, 610, F₂₅₆, 6, 25) (dual of [(610, 6), 3620, 26]-NRT-code)	[i]
3	Digital (15, 40, 610)-net over F₂₅₆	[i]