Best Known (122, 147, s)-Nets in Base 8
(122, 147, 43691)-Net over F8 — Constructive and digital
Digital (122, 147, 43691)-net over F8, using
- 81 times duplication [i] based on digital (121, 146, 43691)-net over F8, using
- net defined by OOA [i] based on linear OOA(8146, 43691, F8, 25, 25) (dual of [(43691, 25), 1092129, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8146, 524293, F8, 25) (dual of [524293, 524147, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8146, 524294, F8, 25) (dual of [524294, 524148, 26]-code), using
- trace code [i] based on linear OA(6473, 262147, F64, 25) (dual of [262147, 262074, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(24) ⊂ Ce(23) [i] based on
- trace code [i] based on linear OA(6473, 262147, F64, 25) (dual of [262147, 262074, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8146, 524294, F8, 25) (dual of [524294, 524148, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8146, 524293, F8, 25) (dual of [524293, 524147, 26]-code), using
- net defined by OOA [i] based on linear OOA(8146, 43691, F8, 25, 25) (dual of [(43691, 25), 1092129, 26]-NRT-code), using
(122, 147, 524296)-Net over F8 — Digital
Digital (122, 147, 524296)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8147, 524296, F8, 25) (dual of [524296, 524149, 26]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8146, 524294, F8, 25) (dual of [524294, 524148, 26]-code), using
- trace code [i] based on linear OA(6473, 262147, F64, 25) (dual of [262147, 262074, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(24) ⊂ Ce(23) [i] based on
- trace code [i] based on linear OA(6473, 262147, F64, 25) (dual of [262147, 262074, 26]-code), using
- linear OA(8146, 524295, F8, 24) (dual of [524295, 524149, 25]-code), using Gilbert–Varšamov bound and bm = 8146 > Vbs−1(k−1) = 375 643654 713268 927017 578910 745687 351564 355732 673691 343865 467946 084799 822383 679833 159903 549379 579596 483050 949605 231283 257301 532672 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(8146, 524294, F8, 25) (dual of [524294, 524148, 26]-code), using
- construction X with Varšamov bound [i] based on
(122, 147, large)-Net in Base 8 — Upper bound on s
There is no (122, 147, large)-net in base 8, because
- 23 times m-reduction [i] would yield (122, 124, large)-net in base 8, but