Best Known (80−14, 80, s)-Nets in Base 8
(80−14, 80, 74899)-Net over F8 — Constructive and digital
Digital (66, 80, 74899)-net over F8, using
- net defined by OOA [i] based on linear OOA(880, 74899, F8, 14, 14) (dual of [(74899, 14), 1048506, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(880, 524293, F8, 14) (dual of [524293, 524213, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(880, 524294, F8, 14) (dual of [524294, 524214, 15]-code), using
- trace code [i] based on linear OA(6440, 262147, F64, 14) (dual of [262147, 262107, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(6437, 262144, F64, 13) (dual of [262144, 262107, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(13) ⊂ Ce(12) [i] based on
- trace code [i] based on linear OA(6440, 262147, F64, 14) (dual of [262147, 262107, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(880, 524294, F8, 14) (dual of [524294, 524214, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(880, 524293, F8, 14) (dual of [524293, 524213, 15]-code), using
(80−14, 80, 524294)-Net over F8 — Digital
Digital (66, 80, 524294)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(880, 524294, F8, 14) (dual of [524294, 524214, 15]-code), using
- trace code [i] based on linear OA(6440, 262147, F64, 14) (dual of [262147, 262107, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(6437, 262144, F64, 13) (dual of [262144, 262107, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(13) ⊂ Ce(12) [i] based on
- trace code [i] based on linear OA(6440, 262147, F64, 14) (dual of [262147, 262107, 15]-code), using
(80−14, 80, large)-Net in Base 8 — Upper bound on s
There is no (66, 80, large)-net in base 8, because
- 12 times m-reduction [i] would yield (66, 68, large)-net in base 8, but