Best Known (132, 170, s)-Nets in Base 8
(132, 170, 1725)-Net over F8 — Constructive and digital
Digital (132, 170, 1725)-net over F8, using
- 83 times duplication [i] based on digital (129, 167, 1725)-net over F8, using
- net defined by OOA [i] based on linear OOA(8167, 1725, F8, 38, 38) (dual of [(1725, 38), 65383, 39]-NRT-code), using
- OA 19-folding and stacking [i] based on linear OA(8167, 32775, F8, 38) (dual of [32775, 32608, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(8167, 32779, F8, 38) (dual of [32779, 32612, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(35) [i] based on
- linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(37) ⊂ Ce(35) [i] based on
- discarding factors / shortening the dual code based on linear OA(8167, 32779, F8, 38) (dual of [32779, 32612, 39]-code), using
- OA 19-folding and stacking [i] based on linear OA(8167, 32775, F8, 38) (dual of [32775, 32608, 39]-code), using
- net defined by OOA [i] based on linear OOA(8167, 1725, F8, 38, 38) (dual of [(1725, 38), 65383, 39]-NRT-code), using
(132, 170, 32792)-Net over F8 — Digital
Digital (132, 170, 32792)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8170, 32792, F8, 38) (dual of [32792, 32622, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
- linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(84, 24, F8, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,8)), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
(132, 170, large)-Net in Base 8 — Upper bound on s
There is no (132, 170, large)-net in base 8, because
- 36 times m-reduction [i] would yield (132, 134, large)-net in base 8, but