Best Known (122−27, 122, s)-Nets in Base 8
(122−27, 122, 2522)-Net over F8 — Constructive and digital
Digital (95, 122, 2522)-net over F8, using
- 82 times duplication [i] based on digital (93, 120, 2522)-net over F8, using
- net defined by OOA [i] based on linear OOA(8120, 2522, F8, 27, 27) (dual of [(2522, 27), 67974, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8120, 32787, F8, 27) (dual of [32787, 32667, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8101, 32768, F8, 23) (dual of [32768, 32667, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(84, 19, F8, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,8)), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- OOA 13-folding and stacking with additional row [i] based on linear OA(8120, 32787, F8, 27) (dual of [32787, 32667, 28]-code), using
- net defined by OOA [i] based on linear OOA(8120, 2522, F8, 27, 27) (dual of [(2522, 27), 67974, 28]-NRT-code), using
(122−27, 122, 32794)-Net over F8 — Digital
Digital (95, 122, 32794)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8122, 32794, F8, 27) (dual of [32794, 32672, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(21) [i] based on
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(86, 26, F8, 4) (dual of [26, 20, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(26) ⊂ Ce(21) [i] based on
(122−27, 122, large)-Net in Base 8 — Upper bound on s
There is no (95, 122, large)-net in base 8, because
- 25 times m-reduction [i] would yield (95, 97, large)-net in base 8, but