Best Known (157−36, 157, s)-Nets in Base 8
(157−36, 157, 1821)-Net over F8 — Constructive and digital
Digital (121, 157, 1821)-net over F8, using
- net defined by OOA [i] based on linear OOA(8157, 1821, F8, 36, 36) (dual of [(1821, 36), 65399, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(8157, 32778, F8, 36) (dual of [32778, 32621, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(8157, 32779, F8, 36) (dual of [32779, 32622, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(33) [i] based on
- linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(35) ⊂ Ce(33) [i] based on
- discarding factors / shortening the dual code based on linear OA(8157, 32779, F8, 36) (dual of [32779, 32622, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(8157, 32778, F8, 36) (dual of [32778, 32621, 37]-code), using
(157−36, 157, 26892)-Net over F8 — Digital
Digital (121, 157, 26892)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8157, 26892, F8, 36) (dual of [26892, 26735, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(8157, 32779, F8, 36) (dual of [32779, 32622, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(33) [i] based on
- linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(35) ⊂ Ce(33) [i] based on
- discarding factors / shortening the dual code based on linear OA(8157, 32779, F8, 36) (dual of [32779, 32622, 37]-code), using
(157−36, 157, large)-Net in Base 8 — Upper bound on s
There is no (121, 157, large)-net in base 8, because
- 34 times m-reduction [i] would yield (121, 123, large)-net in base 8, but