Best Known (131, 158, s)-Nets in Base 8
(131, 158, 40330)-Net over F8 — Constructive and digital
Digital (131, 158, 40330)-net over F8, using
- net defined by OOA [i] based on linear OOA(8158, 40330, F8, 27, 27) (dual of [(40330, 27), 1088752, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8158, 524291, F8, 27) (dual of [524291, 524133, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8158, 524294, F8, 27) (dual of [524294, 524136, 28]-code), using
- trace code [i] based on linear OA(6479, 262147, F64, 27) (dual of [262147, 262068, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(6479, 262144, F64, 27) (dual of [262144, 262065, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- trace code [i] based on linear OA(6479, 262147, F64, 27) (dual of [262147, 262068, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8158, 524294, F8, 27) (dual of [524294, 524136, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8158, 524291, F8, 27) (dual of [524291, 524133, 28]-code), using
(131, 158, 524294)-Net over F8 — Digital
Digital (131, 158, 524294)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8158, 524294, F8, 27) (dual of [524294, 524136, 28]-code), using
- trace code [i] based on linear OA(6479, 262147, F64, 27) (dual of [262147, 262068, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(6479, 262144, F64, 27) (dual of [262144, 262065, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- trace code [i] based on linear OA(6479, 262147, F64, 27) (dual of [262147, 262068, 28]-code), using
(131, 158, large)-Net in Base 8 — Upper bound on s
There is no (131, 158, large)-net in base 8, because
- 25 times m-reduction [i] would yield (131, 133, large)-net in base 8, but