Best Known (107, 107+26, s)-Nets in Base 8
(107, 107+26, 20165)-Net over F8 — Constructive and digital
Digital (107, 133, 20165)-net over F8, using
- net defined by OOA [i] based on linear OOA(8133, 20165, F8, 26, 26) (dual of [(20165, 26), 524157, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8133, 262145, F8, 26) (dual of [262145, 262012, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8133, 262150, F8, 26) (dual of [262150, 262017, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(8133, 262144, F8, 26) (dual of [262144, 262011, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(80, 6, F8, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(8133, 262150, F8, 26) (dual of [262150, 262017, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(8133, 262145, F8, 26) (dual of [262145, 262012, 27]-code), using
(107, 107+26, 131075)-Net over F8 — Digital
Digital (107, 133, 131075)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8133, 131075, F8, 2, 26) (dual of [(131075, 2), 262017, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8133, 262150, F8, 26) (dual of [262150, 262017, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(8133, 262144, F8, 26) (dual of [262144, 262011, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(80, 6, F8, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- OOA 2-folding [i] based on linear OA(8133, 262150, F8, 26) (dual of [262150, 262017, 27]-code), using
(107, 107+26, large)-Net in Base 8 — Upper bound on s
There is no (107, 133, large)-net in base 8, because
- 24 times m-reduction [i] would yield (107, 109, large)-net in base 8, but