Best Known (119, 143, s)-Nets in Base 5
(119, 143, 6514)-Net over F5 — Constructive and digital
Digital (119, 143, 6514)-net over F5, using
- net defined by OOA [i] based on linear OOA(5143, 6514, F5, 24, 24) (dual of [(6514, 24), 156193, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(5143, 78168, F5, 24) (dual of [78168, 78025, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5143, 78169, F5, 24) (dual of [78169, 78026, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(5134, 78125, F5, 24) (dual of [78125, 77991, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5143, 78169, F5, 24) (dual of [78169, 78026, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(5143, 78168, F5, 24) (dual of [78168, 78025, 25]-code), using
(119, 143, 73491)-Net over F5 — Digital
Digital (119, 143, 73491)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5143, 73491, F5, 24) (dual of [73491, 73348, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5143, 78169, F5, 24) (dual of [78169, 78026, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(5134, 78125, F5, 24) (dual of [78125, 77991, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5143, 78169, F5, 24) (dual of [78169, 78026, 25]-code), using
(119, 143, large)-Net in Base 5 — Upper bound on s
There is no (119, 143, large)-net in base 5, because
- 22 times m-reduction [i] would yield (119, 121, large)-net in base 5, but