Best Known (101, 101+26, s)-Nets in Base 5
(101, 101+26, 1204)-Net over F5 — Constructive and digital
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
(101, 101+26, 11435)-Net over F5 — Digital
Digital (101, 127, 11435)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5127, 11435, F5, 26) (dual of [11435, 11308, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5127, 15651, F5, 26) (dual of [15651, 15524, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(21) ⊂ 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(5103, 15625, F5, 22) (dual of [15625, 15522, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(54, 24, F5, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,5)), using
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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 XX applied to Ce(25) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(5127, 15651, F5, 26) (dual of [15651, 15524, 27]-code), using
(101, 101+26, large)-Net in Base 5 — Upper bound on s
There is no (101, 127, large)-net in base 5, because
- 24 times m-reduction [i] would yield (101, 103, large)-net in base 5, but