Best Known (152−24, 152, s)-Nets in Base 8
(152−24, 152, 174765)-Net over F8 — Constructive and digital
Digital (128, 152, 174765)-net over F8, using
- net defined by OOA [i] based on linear OOA(8152, 174765, F8, 24, 24) (dual of [(174765, 24), 4194208, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(8152, 2097180, F8, 24) (dual of [2097180, 2097028, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8152, 2097184, F8, 24) (dual of [2097184, 2097032, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(8152, 2097184, F8, 24) (dual of [2097184, 2097032, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(8152, 2097180, F8, 24) (dual of [2097180, 2097028, 25]-code), using
(152−24, 152, 2042836)-Net over F8 — Digital
Digital (128, 152, 2042836)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8152, 2042836, F8, 24) (dual of [2042836, 2042684, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8152, 2097184, F8, 24) (dual of [2097184, 2097032, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(8152, 2097184, F8, 24) (dual of [2097184, 2097032, 25]-code), using
(152−24, 152, large)-Net in Base 8 — Upper bound on s
There is no (128, 152, large)-net in base 8, because
- 22 times m-reduction [i] would yield (128, 130, large)-net in base 8, but