Best Known (147−29, 147, s)-Nets in Base 5
(147−29, 147, 1118)-Net over F5 — Constructive and digital
Digital (118, 147, 1118)-net over F5, using
- 52 times duplication [i] based on digital (116, 145, 1118)-net over F5, using
- net defined by OOA [i] based on linear OOA(5145, 1118, F5, 29, 29) (dual of [(1118, 29), 32277, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(5145, 15653, F5, 29) (dual of [15653, 15508, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(5145, 15655, F5, 29) (dual of [15655, 15510, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(23) [i] based on
- linear OA(5139, 15625, F5, 29) (dual of [15625, 15486, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(28) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(5145, 15655, F5, 29) (dual of [15655, 15510, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(5145, 15653, F5, 29) (dual of [15653, 15508, 30]-code), using
- net defined by OOA [i] based on linear OOA(5145, 1118, F5, 29, 29) (dual of [(1118, 29), 32277, 30]-NRT-code), using
(147−29, 147, 15658)-Net over F5 — Digital
Digital (118, 147, 15658)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5147, 15658, F5, 29) (dual of [15658, 15511, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- linear OA(5139, 15625, F5, 29) (dual of [15625, 15486, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 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(58, 33, F5, 5) (dual of [33, 25, 6]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
(147−29, 147, large)-Net in Base 5 — Upper bound on s
There is no (118, 147, large)-net in base 5, because
- 27 times m-reduction [i] would yield (118, 120, large)-net in base 5, but