Best Known (128−27, 128, s)-Nets in Base 5
(128−27, 128, 1202)-Net over F5 — Constructive and digital
Digital (101, 128, 1202)-net over F5, using
- 51 times duplication [i] based on digital (100, 127, 1202)-net over F5, using
- net defined by OOA [i] based on linear OOA(5127, 1202, F5, 27, 27) (dual of [(1202, 27), 32327, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(5127, 15627, F5, 27) (dual of [15627, 15500, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(5127, 15631, F5, 27) (dual of [15631, 15504, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(5127, 15625, F5, 27) (dual of [15625, 15498, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(50, 6, F5, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(5127, 15631, F5, 27) (dual of [15631, 15504, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(5127, 15627, F5, 27) (dual of [15627, 15500, 28]-code), using
- net defined by OOA [i] based on linear OOA(5127, 1202, F5, 27, 27) (dual of [(1202, 27), 32327, 28]-NRT-code), using
(128−27, 128, 9026)-Net over F5 — Digital
Digital (101, 128, 9026)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5128, 9026, F5, 27) (dual of [9026, 8898, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(5128, 15632, F5, 27) (dual of [15632, 15504, 28]-code), using
- 1 times code embedding in larger space [i] based on linear OA(5127, 15631, F5, 27) (dual of [15631, 15504, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(5127, 15625, F5, 27) (dual of [15625, 15498, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(50, 6, F5, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(5127, 15631, F5, 27) (dual of [15631, 15504, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(5128, 15632, F5, 27) (dual of [15632, 15504, 28]-code), using
(128−27, 128, large)-Net in Base 5 — Upper bound on s
There is no (101, 128, large)-net in base 5, because
- 25 times m-reduction [i] would yield (101, 103, large)-net in base 5, but