Best Known (146, 166, s)-Nets in Base 4
(146, 166, 419431)-Net over F4 — Constructive and digital
Digital (146, 166, 419431)-net over F4, using
- net defined by OOA [i] based on linear OOA(4166, 419431, F4, 20, 20) (dual of [(419431, 20), 8388454, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(4166, 4194310, F4, 20) (dual of [4194310, 4194144, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4166, 4194315, F4, 20) (dual of [4194315, 4194149, 21]-code), using
- 1 times truncation [i] based on linear OA(4167, 4194316, F4, 21) (dual of [4194316, 4194149, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4155, 4194304, F4, 19) (dual of [4194304, 4194149, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(41, 12, F4, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(4167, 4194316, F4, 21) (dual of [4194316, 4194149, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4166, 4194315, F4, 20) (dual of [4194315, 4194149, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(4166, 4194310, F4, 20) (dual of [4194310, 4194144, 21]-code), using
(146, 166, 1537901)-Net over F4 — Digital
Digital (146, 166, 1537901)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4166, 1537901, F4, 2, 20) (dual of [(1537901, 2), 3075636, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4166, 2097157, F4, 2, 20) (dual of [(2097157, 2), 4194148, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4166, 4194314, F4, 20) (dual of [4194314, 4194148, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4166, 4194315, F4, 20) (dual of [4194315, 4194149, 21]-code), using
- 1 times truncation [i] based on linear OA(4167, 4194316, F4, 21) (dual of [4194316, 4194149, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4155, 4194304, F4, 19) (dual of [4194304, 4194149, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(41, 12, F4, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(4167, 4194316, F4, 21) (dual of [4194316, 4194149, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4166, 4194315, F4, 20) (dual of [4194315, 4194149, 21]-code), using
- OOA 2-folding [i] based on linear OA(4166, 4194314, F4, 20) (dual of [4194314, 4194148, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(4166, 2097157, F4, 2, 20) (dual of [(2097157, 2), 4194148, 21]-NRT-code), using
(146, 166, large)-Net in Base 4 — Upper bound on s
There is no (146, 166, large)-net in base 4, because
- 18 times m-reduction [i] would yield (146, 148, large)-net in base 4, but