Best Known (156, 156+26, s)-Nets in Base 4
(156, 156+26, 20168)-Net over F4 — Constructive and digital
Digital (156, 182, 20168)-net over F4, using
- 43 times duplication [i] based on digital (153, 179, 20168)-net over F4, using
- net defined by OOA [i] based on linear OOA(4179, 20168, F4, 26, 26) (dual of [(20168, 26), 524189, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(4179, 262184, F4, 26) (dual of [262184, 262005, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4179, 262187, F4, 26) (dual of [262187, 262008, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [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(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, 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
- discarding factors / shortening the dual code based on linear OA(4179, 262187, F4, 26) (dual of [262187, 262008, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(4179, 262184, F4, 26) (dual of [262184, 262005, 27]-code), using
- net defined by OOA [i] based on linear OOA(4179, 20168, F4, 26, 26) (dual of [(20168, 26), 524189, 27]-NRT-code), using
(156, 156+26, 131095)-Net over F4 — Digital
Digital (156, 182, 131095)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4182, 131095, F4, 2, 26) (dual of [(131095, 2), 262008, 27]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4180, 131094, F4, 2, 26) (dual of [(131094, 2), 262008, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4180, 262188, F4, 26) (dual of [262188, 262008, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4179, 262187, F4, 26) (dual of [262187, 262008, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [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(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, 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
- 1 times code embedding in larger space [i] based on linear OA(4179, 262187, F4, 26) (dual of [262187, 262008, 27]-code), using
- OOA 2-folding [i] based on linear OA(4180, 262188, F4, 26) (dual of [262188, 262008, 27]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4180, 131094, F4, 2, 26) (dual of [(131094, 2), 262008, 27]-NRT-code), using
(156, 156+26, large)-Net in Base 4 — Upper bound on s
There is no (156, 182, large)-net in base 4, because
- 24 times m-reduction [i] would yield (156, 158, large)-net in base 4, but