Best Known (204, 204+27, s)-Nets in Base 4
(204, 204+27, 322643)-Net over F4 — Constructive and digital
Digital (204, 231, 322643)-net over F4, using
- net defined by OOA [i] based on linear OOA(4231, 322643, F4, 27, 27) (dual of [(322643, 27), 8711130, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4231, 4194360, F4, 27) (dual of [4194360, 4194129, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4231, 4194368, F4, 27) (dual of [4194368, 4194137, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- linear OA(4221, 4194304, F4, 27) (dual of [4194304, 4194083, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(410, 64, F4, 5) (dual of [64, 54, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4231, 4194368, F4, 27) (dual of [4194368, 4194137, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4231, 4194360, F4, 27) (dual of [4194360, 4194129, 28]-code), using
(204, 204+27, 1815067)-Net over F4 — Digital
Digital (204, 231, 1815067)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4231, 1815067, F4, 2, 27) (dual of [(1815067, 2), 3629903, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4231, 2097184, F4, 2, 27) (dual of [(2097184, 2), 4194137, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4231, 4194368, F4, 27) (dual of [4194368, 4194137, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- linear OA(4221, 4194304, F4, 27) (dual of [4194304, 4194083, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(410, 64, F4, 5) (dual of [64, 54, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- OOA 2-folding [i] based on linear OA(4231, 4194368, F4, 27) (dual of [4194368, 4194137, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(4231, 2097184, F4, 2, 27) (dual of [(2097184, 2), 4194137, 28]-NRT-code), using
(204, 204+27, large)-Net in Base 4 — Upper bound on s
There is no (204, 231, large)-net in base 4, because
- 25 times m-reduction [i] would yield (204, 206, large)-net in base 4, but