Best Known (217, 243, s)-Nets in Base 3
(217, 243, 367923)-Net over F3 — Constructive and digital
Digital (217, 243, 367923)-net over F3, using
- net defined by OOA [i] based on linear OOA(3243, 367923, F3, 26, 26) (dual of [(367923, 26), 9565755, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3243, 4782999, F3, 26) (dual of [4782999, 4782756, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3243, 4783001, F3, 26) (dual of [4783001, 4782758, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(3239, 4782969, F3, 26) (dual of [4782969, 4782730, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3211, 4782969, F3, 23) (dual of [4782969, 4782758, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(34, 32, F3, 2) (dual of [32, 28, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3243, 4783001, F3, 26) (dual of [4783001, 4782758, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3243, 4782999, F3, 26) (dual of [4782999, 4782756, 27]-code), using
(217, 243, 1168287)-Net over F3 — Digital
Digital (217, 243, 1168287)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3243, 1168287, F3, 4, 26) (dual of [(1168287, 4), 4672905, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3243, 1195750, F3, 4, 26) (dual of [(1195750, 4), 4782757, 27]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3243, 4783000, F3, 26) (dual of [4783000, 4782757, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3243, 4783001, F3, 26) (dual of [4783001, 4782758, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(3239, 4782969, F3, 26) (dual of [4782969, 4782730, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3211, 4782969, F3, 23) (dual of [4782969, 4782758, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(34, 32, F3, 2) (dual of [32, 28, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3243, 4783001, F3, 26) (dual of [4783001, 4782758, 27]-code), using
- OOA 4-folding [i] based on linear OA(3243, 4783000, F3, 26) (dual of [4783000, 4782757, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(3243, 1195750, F3, 4, 26) (dual of [(1195750, 4), 4782757, 27]-NRT-code), using
(217, 243, large)-Net in Base 3 — Upper bound on s
There is no (217, 243, large)-net in base 3, because
- 24 times m-reduction [i] would yield (217, 219, large)-net in base 3, but