Best Known (175−26, 175, s)-Nets in Base 4
(175−26, 175, 20166)-Net over F4 — Constructive and digital
Digital (149, 175, 20166)-net over F4, using
- net defined by OOA [i] based on linear OOA(4175, 20166, F4, 26, 26) (dual of [(20166, 26), 524141, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(4175, 262158, F4, 26) (dual of [262158, 261983, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4175, 262165, F4, 26) (dual of [262165, 261990, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(4172, 262144, F4, 26) (dual of [262144, 261972, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4154, 262144, F4, 23) (dual of [262144, 261990, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(4175, 262165, F4, 26) (dual of [262165, 261990, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(4175, 262158, F4, 26) (dual of [262158, 261983, 27]-code), using
(175−26, 175, 106120)-Net over F4 — Digital
Digital (149, 175, 106120)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4175, 106120, F4, 2, 26) (dual of [(106120, 2), 212065, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4175, 131082, F4, 2, 26) (dual of [(131082, 2), 261989, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4175, 262164, F4, 26) (dual of [262164, 261989, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4175, 262165, F4, 26) (dual of [262165, 261990, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(4172, 262144, F4, 26) (dual of [262144, 261972, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4154, 262144, F4, 23) (dual of [262144, 261990, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(4175, 262165, F4, 26) (dual of [262165, 261990, 27]-code), using
- OOA 2-folding [i] based on linear OA(4175, 262164, F4, 26) (dual of [262164, 261989, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(4175, 131082, F4, 2, 26) (dual of [(131082, 2), 261989, 27]-NRT-code), using
(175−26, 175, large)-Net in Base 4 — Upper bound on s
There is no (149, 175, large)-net in base 4, because
- 24 times m-reduction [i] would yield (149, 151, large)-net in base 4, but