Best Known (104, 130, s)-Nets in Base 5
(104, 130, 1204)-Net over F5 — Constructive and digital
Digital (104, 130, 1204)-net over F5, using
- 53 times duplication [i] based on digital (101, 127, 1204)-net over F5, using
- net defined by OOA [i] based on linear OOA(5127, 1204, F5, 26, 26) (dual of [(1204, 26), 31177, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(5127, 15652, F5, 26) (dual of [15652, 15525, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5127, 15655, F5, 26) (dual of [15655, 15528, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(5127, 15655, F5, 26) (dual of [15655, 15528, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(5127, 15652, F5, 26) (dual of [15652, 15525, 27]-code), using
- net defined by OOA [i] based on linear OOA(5127, 1204, F5, 26, 26) (dual of [(1204, 26), 31177, 27]-NRT-code), using
(104, 130, 13988)-Net over F5 — Digital
Digital (104, 130, 13988)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5130, 13988, F5, 26) (dual of [13988, 13858, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5130, 15659, F5, 26) (dual of [15659, 15529, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(57, 32, F5, 4) (dual of [32, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(25) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(5130, 15659, F5, 26) (dual of [15659, 15529, 27]-code), using
(104, 130, large)-Net in Base 5 — Upper bound on s
There is no (104, 130, large)-net in base 5, because
- 24 times m-reduction [i] would yield (104, 106, large)-net in base 5, but