Best Known (184−23, 184, s)-Nets in Base 3
(184−23, 184, 48314)-Net over F3 — Constructive and digital
Digital (161, 184, 48314)-net over F3, using
- 31 times duplication [i] based on digital (160, 183, 48314)-net over F3, using
- net defined by OOA [i] based on linear OOA(3183, 48314, F3, 23, 23) (dual of [(48314, 23), 1111039, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3183, 531455, F3, 23) (dual of [531455, 531272, 24]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3181, 531453, F3, 23) (dual of [531453, 531272, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(3181, 531441, F3, 23) (dual of [531441, 531260, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(30, 12, F3, 0) (dual of [12, 12, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3181, 531453, F3, 23) (dual of [531453, 531272, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3183, 531455, F3, 23) (dual of [531455, 531272, 24]-code), using
- net defined by OOA [i] based on linear OOA(3183, 48314, F3, 23, 23) (dual of [(48314, 23), 1111039, 24]-NRT-code), using
(184−23, 184, 139103)-Net over F3 — Digital
Digital (161, 184, 139103)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3184, 139103, F3, 3, 23) (dual of [(139103, 3), 417125, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3184, 177152, F3, 3, 23) (dual of [(177152, 3), 531272, 24]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3181, 177151, F3, 3, 23) (dual of [(177151, 3), 531272, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3181, 531453, F3, 23) (dual of [531453, 531272, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(3181, 531441, F3, 23) (dual of [531441, 531260, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(30, 12, F3, 0) (dual of [12, 12, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- OOA 3-folding [i] based on linear OA(3181, 531453, F3, 23) (dual of [531453, 531272, 24]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3181, 177151, F3, 3, 23) (dual of [(177151, 3), 531272, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3184, 177152, F3, 3, 23) (dual of [(177152, 3), 531272, 24]-NRT-code), using
(184−23, 184, large)-Net in Base 3 — Upper bound on s
There is no (161, 184, large)-net in base 3, because
- 21 times m-reduction [i] would yield (161, 163, large)-net in base 3, but