Best Known (59, 59+14, s)-Nets in Base 5
(59, 59+14, 2236)-Net over F5 — Constructive and digital
Digital (59, 73, 2236)-net over F5, using
- net defined by OOA [i] based on linear OOA(573, 2236, F5, 14, 14) (dual of [(2236, 14), 31231, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(573, 15652, F5, 14) (dual of [15652, 15579, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(573, 15655, F5, 14) (dual of [15655, 15582, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(543, 15625, F5, 9) (dual of [15625, 15582, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(573, 15655, F5, 14) (dual of [15655, 15582, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(573, 15652, F5, 14) (dual of [15652, 15579, 15]-code), using
(59, 59+14, 15655)-Net over F5 — Digital
Digital (59, 73, 15655)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(573, 15655, F5, 14) (dual of [15655, 15582, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(543, 15625, F5, 9) (dual of [15625, 15582, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
(59, 59+14, large)-Net in Base 5 — Upper bound on s
There is no (59, 73, large)-net in base 5, because
- 12 times m-reduction [i] would yield (59, 61, large)-net in base 5, but