Best Known (134, 134+26, s)-Nets in Base 4
(134, 134+26, 5044)-Net over F4 — Constructive and digital
Digital (134, 160, 5044)-net over F4, using
- net defined by OOA [i] based on linear OOA(4160, 5044, F4, 26, 26) (dual of [(5044, 26), 130984, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(4160, 65572, F4, 26) (dual of [65572, 65412, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4160, 65575, F4, 26) (dual of [65575, 65415, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4160, 65575, F4, 26) (dual of [65575, 65415, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(4160, 65572, F4, 26) (dual of [65572, 65412, 27]-code), using
(134, 134+26, 32787)-Net over F4 — Digital
Digital (134, 160, 32787)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4160, 32787, F4, 2, 26) (dual of [(32787, 2), 65414, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4160, 65574, F4, 26) (dual of [65574, 65414, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4160, 65575, F4, 26) (dual of [65575, 65415, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4160, 65575, F4, 26) (dual of [65575, 65415, 27]-code), using
- OOA 2-folding [i] based on linear OA(4160, 65574, F4, 26) (dual of [65574, 65414, 27]-code), using
(134, 134+26, large)-Net in Base 4 — Upper bound on s
There is no (134, 160, large)-net in base 4, because
- 24 times m-reduction [i] would yield (134, 136, large)-net in base 4, but