Best Known (124, 124+26, s)-Nets in Base 5
(124, 124+26, 6012)-Net over F5 — Constructive and digital
Digital (124, 150, 6012)-net over F5, using
- 52 times duplication [i] based on digital (122, 148, 6012)-net over F5, using
- net defined by OOA [i] based on linear OOA(5148, 6012, F5, 26, 26) (dual of [(6012, 26), 156164, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(5148, 78156, F5, 26) (dual of [78156, 78008, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5148, 78160, F5, 26) (dual of [78160, 78012, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [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(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(57, 35, F5, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(5148, 78160, F5, 26) (dual of [78160, 78012, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(5148, 78156, F5, 26) (dual of [78156, 78008, 27]-code), using
- net defined by OOA [i] based on linear OOA(5148, 6012, F5, 26, 26) (dual of [(6012, 26), 156164, 27]-NRT-code), using
(124, 124+26, 53531)-Net over F5 — Digital
Digital (124, 150, 53531)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5150, 53531, F5, 26) (dual of [53531, 53381, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5150, 78162, F5, 26) (dual of [78162, 78012, 27]-code), using
- 2 times code embedding in larger space [i] based on linear OA(5148, 78160, F5, 26) (dual of [78160, 78012, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [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(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(57, 35, F5, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(5148, 78160, F5, 26) (dual of [78160, 78012, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5150, 78162, F5, 26) (dual of [78162, 78012, 27]-code), using
(124, 124+26, large)-Net in Base 5 — Upper bound on s
There is no (124, 150, large)-net in base 5, because
- 24 times m-reduction [i] would yield (124, 126, large)-net in base 5, but