Best Known (100−17, 100, s)-Nets in Base 4
(100−17, 100, 8194)-Net over F4 — Constructive and digital
Digital (83, 100, 8194)-net over F4, using
- net defined by OOA [i] based on linear OOA(4100, 8194, F4, 17, 17) (dual of [(8194, 17), 139198, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(4100, 65553, F4, 17) (dual of [65553, 65453, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4100, 65555, F4, 17) (dual of [65555, 65455, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(481, 65536, F4, 14) (dual of [65536, 65455, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(43, 19, F4, 2) (dual of [19, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(4100, 65555, F4, 17) (dual of [65555, 65455, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(4100, 65553, F4, 17) (dual of [65553, 65453, 18]-code), using
(100−17, 100, 32777)-Net over F4 — Digital
Digital (83, 100, 32777)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4100, 32777, F4, 2, 17) (dual of [(32777, 2), 65454, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4100, 65554, F4, 17) (dual of [65554, 65454, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4100, 65555, F4, 17) (dual of [65555, 65455, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(481, 65536, F4, 14) (dual of [65536, 65455, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(43, 19, F4, 2) (dual of [19, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(4100, 65555, F4, 17) (dual of [65555, 65455, 18]-code), using
- OOA 2-folding [i] based on linear OA(4100, 65554, F4, 17) (dual of [65554, 65454, 18]-code), using
(100−17, 100, large)-Net in Base 4 — Upper bound on s
There is no (83, 100, large)-net in base 4, because
- 15 times m-reduction [i] would yield (83, 85, large)-net in base 4, but