MinT - Information on Result #1616198

Information on Result #1616198

Linear OOA(256⁵¹, 610, F₂₅₆, 4, 32) (dual of [(610, 4), 2389, 33]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(256¹⁷, 289, F₂₅₆, 4, 16) (dual of [(289, 4), 1139, 17]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,1139P) [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(256³⁴, 321, F₂₅₆, 4, 32) (dual of [(321, 4), 1250, 33]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,1251P) [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(256⁵¹, 610, F₂₅₆, 5, 32) (dual of [(610, 5), 2999, 33]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256⁵¹, 610, F₂₅₆, 6, 32) (dual of [(610, 6), 3609, 33]-NRT-code)	[i]
3	Digital (19, 51, 610)-net over F₂₅₆	[i]