Best Known (20, 20+5, s)-Nets in Base 8
(20, 20+5, 131074)-Net over F8 — Constructive and digital
Digital (20, 25, 131074)-net over F8, using
- net defined by OOA [i] based on linear OOA(825, 131074, F8, 5, 5) (dual of [(131074, 5), 655345, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(825, 262149, F8, 5) (dual of [262149, 262124, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(825, 262150, F8, 5) (dual of [262150, 262125, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(825, 262144, F8, 5) (dual of [262144, 262119, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(819, 262144, F8, 4) (dual of [262144, 262125, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(4) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(825, 262150, F8, 5) (dual of [262150, 262125, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(825, 262149, F8, 5) (dual of [262149, 262124, 6]-code), using
(20, 20+5, 262150)-Net over F8 — Digital
Digital (20, 25, 262150)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(825, 262150, F8, 5) (dual of [262150, 262125, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(825, 262144, F8, 5) (dual of [262144, 262119, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(819, 262144, F8, 4) (dual of [262144, 262125, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(4) ⊂ Ce(3) [i] based on
(20, 20+5, large)-Net in Base 8 — Upper bound on s
There is no (20, 25, large)-net in base 8, because
- 3 times m-reduction [i] would yield (20, 22, large)-net in base 8, but