Best Known (199, 199+23, s)-Nets in Base 3
(199, 199+23, 434821)-Net over F3 — Constructive and digital
Digital (199, 222, 434821)-net over F3, using
- net defined by OOA [i] based on linear OOA(3222, 434821, F3, 23, 23) (dual of [(434821, 23), 10000661, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3222, 4783032, F3, 23) (dual of [4783032, 4782810, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3222, 4783036, F3, 23) (dual of [4783036, 4782814, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- 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(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3222, 4783036, F3, 23) (dual of [4783036, 4782814, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3222, 4783032, F3, 23) (dual of [4783032, 4782810, 24]-code), using
(199, 199+23, 1252073)-Net over F3 — Digital
Digital (199, 222, 1252073)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3222, 1252073, F3, 3, 23) (dual of [(1252073, 3), 3755997, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3222, 1594345, F3, 3, 23) (dual of [(1594345, 3), 4782813, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3222, 4783035, F3, 23) (dual of [4783035, 4782813, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3222, 4783036, F3, 23) (dual of [4783036, 4782814, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- 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(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3222, 4783036, F3, 23) (dual of [4783036, 4782814, 24]-code), using
- OOA 3-folding [i] based on linear OA(3222, 4783035, F3, 23) (dual of [4783035, 4782813, 24]-code), using
- discarding factors / shortening the dual code based on linear OOA(3222, 1594345, F3, 3, 23) (dual of [(1594345, 3), 4782813, 24]-NRT-code), using
(199, 199+23, large)-Net in Base 3 — Upper bound on s
There is no (199, 222, large)-net in base 3, because
- 21 times m-reduction [i] would yield (199, 201, large)-net in base 3, but