Best Known (179−26, 179, s)-Nets in Base 4
(179−26, 179, 20168)-Net over F4 — Constructive and digital
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
(179−26, 179, 131093)-Net over F4 — Digital
Digital (153, 179, 131093)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4179, 131093, F4, 2, 26) (dual of [(131093, 2), 262007, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4179, 262186, F4, 26) (dual of [262186, 262007, 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
- OOA 2-folding [i] based on linear OA(4179, 262186, F4, 26) (dual of [262186, 262007, 27]-code), using
(179−26, 179, large)-Net in Base 4 — Upper bound on s
There is no (153, 179, large)-net in base 4, because
- 24 times m-reduction [i] would yield (153, 155, large)-net in base 4, but