Best Known (128, 153, s)-Nets in Base 8
(128, 153, 174764)-Net over F8 — Constructive and digital
Digital (128, 153, 174764)-net over F8, using
- 82 times duplication [i] based on digital (126, 151, 174764)-net over F8, using
- net defined by OOA [i] based on linear OOA(8151, 174764, F8, 25, 25) (dual of [(174764, 25), 4368949, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8151, 2097169, F8, 25) (dual of [2097169, 2097018, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [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(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(83, 17, F8, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(8151, 2097169, F8, 25) (dual of [2097169, 2097018, 26]-code), using
- net defined by OOA [i] based on linear OOA(8151, 174764, F8, 25, 25) (dual of [(174764, 25), 4368949, 26]-NRT-code), using
(128, 153, 1251988)-Net over F8 — Digital
Digital (128, 153, 1251988)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8153, 1251988, F8, 25) (dual of [1251988, 1251835, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8153, 2097179, F8, 25) (dual of [2097179, 2097026, 26]-code), using
- construction XX applied to Ce(24) ⊂ Ce(20) ⊂ 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(8127, 2097152, F8, 21) (dual of [2097152, 2097025, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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, 26, F8, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,8)), using
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(8153, 2097179, F8, 25) (dual of [2097179, 2097026, 26]-code), using
(128, 153, large)-Net in Base 8 — Upper bound on s
There is no (128, 153, large)-net in base 8, because
- 23 times m-reduction [i] would yield (128, 130, large)-net in base 8, but