Best Known (118−23, 118, s)-Nets in Base 5
(118−23, 118, 1423)-Net over F5 — Constructive and digital
Digital (95, 118, 1423)-net over F5, using
- 53 times duplication [i] based on digital (92, 115, 1423)-net over F5, using
- net defined by OOA [i] based on linear OOA(5115, 1423, F5, 23, 23) (dual of [(1423, 23), 32614, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5115, 15654, F5, 23) (dual of [15654, 15539, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(5115, 15655, F5, 23) (dual of [15655, 15540, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(5109, 15625, F5, 23) (dual of [15625, 15516, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5115, 15655, F5, 23) (dual of [15655, 15540, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5115, 15654, F5, 23) (dual of [15654, 15539, 24]-code), using
- net defined by OOA [i] based on linear OOA(5115, 1423, F5, 23, 23) (dual of [(1423, 23), 32614, 24]-NRT-code), using
(118−23, 118, 15664)-Net over F5 — Digital
Digital (95, 118, 15664)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5118, 15664, F5, 23) (dual of [15664, 15546, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(5109, 15625, F5, 23) (dual of [15625, 15516, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(579, 15625, F5, 17) (dual of [15625, 15546, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(59, 39, F5, 5) (dual of [39, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
(118−23, 118, large)-Net in Base 5 — Upper bound on s
There is no (95, 118, large)-net in base 5, because
- 21 times m-reduction [i] would yield (95, 97, large)-net in base 5, but