Best Known (46, 46+14, s)-Nets in Base 5
(46, 46+14, 449)-Net over F5 — Constructive and digital
Digital (46, 60, 449)-net over F5, using
- 51 times duplication [i] based on digital (45, 59, 449)-net over F5, using
- net defined by OOA [i] based on linear OOA(559, 449, F5, 14, 14) (dual of [(449, 14), 6227, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(559, 3143, F5, 14) (dual of [3143, 3084, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(556, 3125, F5, 14) (dual of [3125, 3069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(541, 3125, F5, 11) (dual of [3125, 3084, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(53, 18, F5, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- OA 7-folding and stacking [i] based on linear OA(559, 3143, F5, 14) (dual of [3143, 3084, 15]-code), using
- net defined by OOA [i] based on linear OOA(559, 449, F5, 14, 14) (dual of [(449, 14), 6227, 15]-NRT-code), using
(46, 46+14, 3180)-Net over F5 — Digital
Digital (46, 60, 3180)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(560, 3180, F5, 14) (dual of [3180, 3120, 15]-code), using
- 46 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 11 times 0, 1, 29 times 0) [i] based on linear OA(556, 3130, F5, 14) (dual of [3130, 3074, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(556, 3125, F5, 14) (dual of [3125, 3069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(551, 3125, F5, 13) (dual of [3125, 3074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(50, 5, F5, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- 46 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 11 times 0, 1, 29 times 0) [i] based on linear OA(556, 3130, F5, 14) (dual of [3130, 3074, 15]-code), using
(46, 46+14, 827994)-Net in Base 5 — Upper bound on s
There is no (46, 60, 827995)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 867362 900848 280558 687821 571934 094867 482517 > 560 [i]