Best Known (92, 92+22, s)-Nets in Base 4
(92, 92+22, 1490)-Net over F4 — Constructive and digital
Digital (92, 114, 1490)-net over F4, using
- 41 times duplication [i] based on digital (91, 113, 1490)-net over F4, using
- net defined by OOA [i] based on linear OOA(4113, 1490, F4, 22, 22) (dual of [(1490, 22), 32667, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(4113, 16390, F4, 22) (dual of [16390, 16277, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4113, 16391, F4, 22) (dual of [16391, 16278, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(40, 7, F4, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4113, 16391, F4, 22) (dual of [16391, 16278, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(4113, 16390, F4, 22) (dual of [16390, 16277, 23]-code), using
- net defined by OOA [i] based on linear OOA(4113, 1490, F4, 22, 22) (dual of [(1490, 22), 32667, 23]-NRT-code), using
(92, 92+22, 8196)-Net over F4 — Digital
Digital (92, 114, 8196)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4114, 8196, F4, 2, 22) (dual of [(8196, 2), 16278, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4114, 16392, F4, 22) (dual of [16392, 16278, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4113, 16391, F4, 22) (dual of [16391, 16278, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(40, 7, F4, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4113, 16391, F4, 22) (dual of [16391, 16278, 23]-code), using
- OOA 2-folding [i] based on linear OA(4114, 16392, F4, 22) (dual of [16392, 16278, 23]-code), using
(92, 92+22, 2840680)-Net in Base 4 — Upper bound on s
There is no (92, 114, 2840681)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 431 359920 153782 406668 636874 859118 150081 482991 510701 369791 139966 138720 > 4114 [i]