Best Known (202−25, 202, s)-Nets in Base 4
(202−25, 202, 349527)-Net over F4 — Constructive and digital
Digital (177, 202, 349527)-net over F4, using
- net defined by OOA [i] based on linear OOA(4202, 349527, F4, 25, 25) (dual of [(349527, 25), 8737973, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4202, 4194325, F4, 25) (dual of [4194325, 4194123, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(4199, 4194304, F4, 25) (dual of [4194304, 4194105, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4177, 4194304, F4, 22) (dual of [4194304, 4194127, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(4202, 4194325, F4, 25) (dual of [4194325, 4194123, 26]-code), using
(202−25, 202, 1398108)-Net over F4 — Digital
Digital (177, 202, 1398108)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4202, 1398108, F4, 3, 25) (dual of [(1398108, 3), 4194122, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4202, 4194324, F4, 25) (dual of [4194324, 4194122, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4202, 4194325, F4, 25) (dual of [4194325, 4194123, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(4199, 4194304, F4, 25) (dual of [4194304, 4194105, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4177, 4194304, F4, 22) (dual of [4194304, 4194127, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(4202, 4194325, F4, 25) (dual of [4194325, 4194123, 26]-code), using
- OOA 3-folding [i] based on linear OA(4202, 4194324, F4, 25) (dual of [4194324, 4194122, 26]-code), using
(202−25, 202, large)-Net in Base 4 — Upper bound on s
There is no (177, 202, large)-net in base 4, because
- 23 times m-reduction [i] would yield (177, 179, large)-net in base 4, but