Best Known (144−26, 144, s)-Nets in Base 5
(144−26, 144, 6010)-Net over F5 — Constructive and digital
Digital (118, 144, 6010)-net over F5, using
- 52 times duplication [i] based on digital (116, 142, 6010)-net over F5, using
- net defined by OOA [i] based on linear OOA(5142, 6010, F5, 26, 26) (dual of [(6010, 26), 156118, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(5142, 78130, F5, 26) (dual of [78130, 77988, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5142, 78133, F5, 26) (dual of [78133, 77991, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- linear OA(5141, 78125, F5, 26) (dual of [78125, 77984, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 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(51, 8, F5, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(5142, 78133, F5, 26) (dual of [78133, 77991, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(5142, 78130, F5, 26) (dual of [78130, 77988, 27]-code), using
- net defined by OOA [i] based on linear OOA(5142, 6010, F5, 26, 26) (dual of [(6010, 26), 156118, 27]-NRT-code), using
(144−26, 144, 39071)-Net over F5 — Digital
Digital (118, 144, 39071)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5144, 39071, F5, 2, 26) (dual of [(39071, 2), 77998, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5144, 78142, F5, 26) (dual of [78142, 77998, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- linear OA(5141, 78125, F5, 26) (dual of [78125, 77984, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(5127, 78125, F5, 23) (dual of [78125, 77998, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(53, 17, F5, 2) (dual of [17, 14, 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(25) ⊂ Ce(22) [i] based on
- OOA 2-folding [i] based on linear OA(5144, 78142, F5, 26) (dual of [78142, 77998, 27]-code), using
(144−26, 144, large)-Net in Base 5 — Upper bound on s
There is no (118, 144, large)-net in base 5, because
- 24 times m-reduction [i] would yield (118, 120, large)-net in base 5, but