Best Known (199−26, 199, s)-Nets in Base 3
(199−26, 199, 13630)-Net over F3 — Constructive and digital
Digital (173, 199, 13630)-net over F3, using
- 31 times duplication [i] based on digital (172, 198, 13630)-net over F3, using
- net defined by OOA [i] based on linear OOA(3198, 13630, F3, 26, 26) (dual of [(13630, 26), 354182, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3198, 177190, F3, 26) (dual of [177190, 176992, 27]-code), using
- 4 times code embedding in larger space [i] based on linear OA(3194, 177186, F3, 26) (dual of [177186, 176992, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(3188, 177147, F3, 26) (dual of [177147, 176959, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3155, 177147, F3, 22) (dual of [177147, 176992, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- 4 times code embedding in larger space [i] based on linear OA(3194, 177186, F3, 26) (dual of [177186, 176992, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3198, 177190, F3, 26) (dual of [177190, 176992, 27]-code), using
- net defined by OOA [i] based on linear OOA(3198, 13630, F3, 26, 26) (dual of [(13630, 26), 354182, 27]-NRT-code), using
(199−26, 199, 59067)-Net over F3 — Digital
Digital (173, 199, 59067)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3199, 59067, F3, 3, 26) (dual of [(59067, 3), 177002, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3199, 177201, F3, 26) (dual of [177201, 177002, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3199, 177202, F3, 26) (dual of [177202, 177003, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(3188, 177147, F3, 26) (dual of [177147, 176959, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3144, 177147, F3, 20) (dual of [177147, 177003, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(311, 55, F3, 5) (dual of [55, 44, 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(3199, 177202, F3, 26) (dual of [177202, 177003, 27]-code), using
- OOA 3-folding [i] based on linear OA(3199, 177201, F3, 26) (dual of [177201, 177002, 27]-code), using
(199−26, 199, large)-Net in Base 3 — Upper bound on s
There is no (173, 199, large)-net in base 3, because
- 24 times m-reduction [i] would yield (173, 175, large)-net in base 3, but