Best Known (135, 135+36, s)-Nets in Base 8
(135, 135+36, 1823)-Net over F8 — Constructive and digital
Digital (135, 171, 1823)-net over F8, using
- 82 times duplication [i] based on digital (133, 169, 1823)-net over F8, using
- net defined by OOA [i] based on linear OOA(8169, 1823, F8, 36, 36) (dual of [(1823, 36), 65459, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(8169, 32814, F8, 36) (dual of [32814, 32645, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(8169, 32816, F8, 36) (dual of [32816, 32647, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(27) [i] based on
- 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(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(813, 48, F8, 7) (dual of [48, 35, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using
- construction X applied to Ce(35) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(8169, 32816, F8, 36) (dual of [32816, 32647, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(8169, 32814, F8, 36) (dual of [32814, 32645, 37]-code), using
- net defined by OOA [i] based on linear OOA(8169, 1823, F8, 36, 36) (dual of [(1823, 36), 65459, 37]-NRT-code), using
(135, 135+36, 51351)-Net over F8 — Digital
Digital (135, 171, 51351)-net over F8, using
(135, 135+36, large)-Net in Base 8 — Upper bound on s
There is no (135, 171, large)-net in base 8, because
- 34 times m-reduction [i] would yield (135, 137, large)-net in base 8, but