Best Known (180−30, 180, s)-Nets in Base 4
(180−30, 180, 4370)-Net over F4 — Constructive and digital
Digital (150, 180, 4370)-net over F4, using
- net defined by OOA [i] based on linear OOA(4180, 4370, F4, 30, 30) (dual of [(4370, 30), 130920, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(4180, 65550, F4, 30) (dual of [65550, 65370, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4180, 65555, F4, 30) (dual of [65555, 65375, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- linear OA(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(43, 19, F4, 2) (dual of [19, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(4180, 65555, F4, 30) (dual of [65555, 65375, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(4180, 65550, F4, 30) (dual of [65550, 65370, 31]-code), using
(180−30, 180, 32777)-Net over F4 — Digital
Digital (150, 180, 32777)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4180, 32777, F4, 2, 30) (dual of [(32777, 2), 65374, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4180, 65554, F4, 30) (dual of [65554, 65374, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4180, 65555, F4, 30) (dual of [65555, 65375, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- linear OA(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(43, 19, F4, 2) (dual of [19, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- construction X applied to Ce(29) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(4180, 65555, F4, 30) (dual of [65555, 65375, 31]-code), using
- OOA 2-folding [i] based on linear OA(4180, 65554, F4, 30) (dual of [65554, 65374, 31]-code), using
(180−30, 180, large)-Net in Base 4 — Upper bound on s
There is no (150, 180, large)-net in base 4, because
- 28 times m-reduction [i] would yield (150, 152, large)-net in base 4, but