Best Known (141, 141+26, s)-Nets in Base 8
(141, 141+26, 161323)-Net over F8 — Constructive and digital
Digital (141, 167, 161323)-net over F8, using
- 81 times duplication [i] based on digital (140, 166, 161323)-net over F8, using
- net defined by OOA [i] based on linear OOA(8166, 161323, F8, 26, 26) (dual of [(161323, 26), 4194232, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8166, 2097199, F8, 26) (dual of [2097199, 2097033, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8166, 2097205, F8, 26) (dual of [2097205, 2097039, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8113, 2097152, F8, 19) (dual of [2097152, 2097039, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(811, 53, F8, 6) (dual of [53, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(8166, 2097205, F8, 26) (dual of [2097205, 2097039, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(8166, 2097199, F8, 26) (dual of [2097199, 2097033, 27]-code), using
- net defined by OOA [i] based on linear OOA(8166, 161323, F8, 26, 26) (dual of [(161323, 26), 4194232, 27]-NRT-code), using
(141, 141+26, 2097213)-Net over F8 — Digital
Digital (141, 167, 2097213)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8167, 2097213, F8, 26) (dual of [2097213, 2097046, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(812, 61, F8, 7) (dual of [61, 49, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(812, 73, F8, 7) (dual of [73, 61, 8]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(812, 73, F8, 7) (dual of [73, 61, 8]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
(141, 141+26, large)-Net in Base 8 — Upper bound on s
There is no (141, 167, large)-net in base 8, because
- 24 times m-reduction [i] would yield (141, 143, large)-net in base 8, but