Best Known (101, 115, s)-Nets in Base 4
(101, 115, 599190)-Net over F4 — Constructive and digital
Digital (101, 115, 599190)-net over F4, using
- net defined by OOA [i] based on linear OOA(4115, 599190, F4, 14, 14) (dual of [(599190, 14), 8388545, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(4115, 4194330, F4, 14) (dual of [4194330, 4194215, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(4111, 4194304, F4, 14) (dual of [4194304, 4194193, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(489, 4194304, F4, 11) (dual of [4194304, 4194215, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(44, 26, F4, 2) (dual of [26, 22, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
- Hamming code H(4,4) [i]
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- OA 7-folding and stacking [i] based on linear OA(4115, 4194330, F4, 14) (dual of [4194330, 4194215, 15]-code), using
(101, 115, 2097165)-Net over F4 — Digital
Digital (101, 115, 2097165)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4115, 2097165, F4, 2, 14) (dual of [(2097165, 2), 4194215, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4115, 4194330, F4, 14) (dual of [4194330, 4194215, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(4111, 4194304, F4, 14) (dual of [4194304, 4194193, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(489, 4194304, F4, 11) (dual of [4194304, 4194215, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(44, 26, F4, 2) (dual of [26, 22, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
- Hamming code H(4,4) [i]
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- OOA 2-folding [i] based on linear OA(4115, 4194330, F4, 14) (dual of [4194330, 4194215, 15]-code), using
(101, 115, large)-Net in Base 4 — Upper bound on s
There is no (101, 115, large)-net in base 4, because
- 12 times m-reduction [i] would yield (101, 103, large)-net in base 4, but