Best Known (159−26, 159, s)-Nets in Base 8
(159−26, 159, 161321)-Net over F8 — Constructive and digital
Digital (133, 159, 161321)-net over F8, using
- net defined by OOA [i] based on linear OOA(8159, 161321, F8, 26, 26) (dual of [(161321, 26), 4194187, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8159, 2097173, F8, 26) (dual of [2097173, 2097014, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8159, 2097177, F8, 26) (dual of [2097177, 2097018, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [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(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(84, 25, F8, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,8)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8159, 2097177, F8, 26) (dual of [2097177, 2097018, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(8159, 2097173, F8, 26) (dual of [2097173, 2097014, 27]-code), using
(159−26, 159, 1234815)-Net over F8 — Digital
Digital (133, 159, 1234815)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8159, 1234815, F8, 26) (dual of [1234815, 1234656, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8159, 2097177, F8, 26) (dual of [2097177, 2097018, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [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(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(84, 25, F8, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,8)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8159, 2097177, F8, 26) (dual of [2097177, 2097018, 27]-code), using
(159−26, 159, large)-Net in Base 8 — Upper bound on s
There is no (133, 159, large)-net in base 8, because
- 24 times m-reduction [i] would yield (133, 135, large)-net in base 8, but