Best Known (199−26, 199, s)-Nets in Base 4
(199−26, 199, 80663)-Net over F4 — Constructive and digital
Digital (173, 199, 80663)-net over F4, using
- 41 times duplication [i] based on digital (172, 198, 80663)-net over F4, using
- net defined by OOA [i] based on linear OOA(4198, 80663, F4, 26, 26) (dual of [(80663, 26), 2097040, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(4198, 1048619, F4, 26) (dual of [1048619, 1048421, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(4191, 1048576, F4, 26) (dual of [1048576, 1048385, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- OA 13-folding and stacking [i] based on linear OA(4198, 1048619, F4, 26) (dual of [1048619, 1048421, 27]-code), using
- net defined by OOA [i] based on linear OOA(4198, 80663, F4, 26, 26) (dual of [(80663, 26), 2097040, 27]-NRT-code), using
(199−26, 199, 450912)-Net over F4 — Digital
Digital (173, 199, 450912)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4199, 450912, F4, 2, 26) (dual of [(450912, 2), 901625, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4199, 524312, F4, 2, 26) (dual of [(524312, 2), 1048425, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4199, 1048624, F4, 26) (dual of [1048624, 1048425, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(4191, 1048576, F4, 26) (dual of [1048576, 1048385, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(48, 48, F4, 4) (dual of [48, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- OOA 2-folding [i] based on linear OA(4199, 1048624, F4, 26) (dual of [1048624, 1048425, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(4199, 524312, F4, 2, 26) (dual of [(524312, 2), 1048425, 27]-NRT-code), using
(199−26, 199, large)-Net in Base 4 — Upper bound on s
There is no (173, 199, large)-net in base 4, because
- 24 times m-reduction [i] would yield (173, 175, large)-net in base 4, but