Best Known (250−26, 250, s)-Nets in Base 3
(250−26, 250, 367925)-Net over F3 — Constructive and digital
Digital (224, 250, 367925)-net over F3, using
- net defined by OOA [i] based on linear OOA(3250, 367925, F3, 26, 26) (dual of [(367925, 26), 9565800, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3250, 4783025, F3, 26) (dual of [4783025, 4782775, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3250, 4783036, F3, 26) (dual of [4783036, 4782786, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [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(3183, 4782969, F3, 20) (dual of [4782969, 4782786, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(311, 67, F3, 5) (dual of [67, 56, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3250, 4783036, F3, 26) (dual of [4783036, 4782786, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3250, 4783025, F3, 26) (dual of [4783025, 4782775, 27]-code), using
(250−26, 250, 1195759)-Net over F3 — Digital
Digital (224, 250, 1195759)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3250, 1195759, F3, 4, 26) (dual of [(1195759, 4), 4782786, 27]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3250, 4783036, F3, 26) (dual of [4783036, 4782786, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [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(3183, 4782969, F3, 20) (dual of [4782969, 4782786, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(311, 67, F3, 5) (dual of [67, 56, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- OOA 4-folding [i] based on linear OA(3250, 4783036, F3, 26) (dual of [4783036, 4782786, 27]-code), using
(250−26, 250, large)-Net in Base 3 — Upper bound on s
There is no (224, 250, large)-net in base 3, because
- 24 times m-reduction [i] would yield (224, 226, large)-net in base 3, but