Best Known (100, 126, s)-Nets in Base 5
(100, 126, 1203)-Net over F5 — Constructive and digital
Digital (100, 126, 1203)-net over F5, using
- 52 times duplication [i] based on digital (98, 124, 1203)-net over F5, using
- net defined by OOA [i] based on linear OOA(5124, 1203, F5, 26, 26) (dual of [(1203, 26), 31154, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(5124, 15639, F5, 26) (dual of [15639, 15515, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5124, 15640, F5, 26) (dual of [15640, 15516, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [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(5109, 15625, F5, 23) (dual of [15625, 15516, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(53, 15, F5, 2) (dual of [15, 12, 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
- discarding factors / shortening the dual code based on linear OA(5124, 15640, F5, 26) (dual of [15640, 15516, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(5124, 15639, F5, 26) (dual of [15639, 15515, 27]-code), using
- net defined by OOA [i] based on linear OOA(5124, 1203, F5, 26, 26) (dual of [(1203, 26), 31154, 27]-NRT-code), using
(100, 126, 10693)-Net over F5 — Digital
Digital (100, 126, 10693)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5126, 10693, F5, 26) (dual of [10693, 10567, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5126, 15649, F5, 26) (dual of [15649, 15523, 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, 23, F5, 3) (dual of [23, 19, 4]-code or 23-cap in PG(3,5)), using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(25) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(5126, 15649, F5, 26) (dual of [15649, 15523, 27]-code), using
(100, 126, large)-Net in Base 5 — Upper bound on s
There is no (100, 126, large)-net in base 5, because
- 24 times m-reduction [i] would yield (100, 102, large)-net in base 5, but