Best Known (104, 104+27, s)-Nets in Base 5
(104, 104+27, 1203)-Net over F5 — Constructive and digital
Digital (104, 131, 1203)-net over F5, using
- 51 times duplication [i] based on digital (103, 130, 1203)-net over F5, using
- net defined by OOA [i] based on linear OOA(5130, 1203, F5, 27, 27) (dual of [(1203, 27), 32351, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(5130, 15640, F5, 27) (dual of [15640, 15510, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(23) [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(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(26) ⊂ Ce(23) [i] based on
- OOA 13-folding and stacking with additional row [i] based on linear OA(5130, 15640, F5, 27) (dual of [15640, 15510, 28]-code), using
- net defined by OOA [i] based on linear OOA(5130, 1203, F5, 27, 27) (dual of [(1203, 27), 32351, 28]-NRT-code), using
(104, 104+27, 10952)-Net over F5 — Digital
Digital (104, 131, 10952)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5131, 10952, F5, 27) (dual of [10952, 10821, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(5131, 15647, F5, 27) (dual of [15647, 15516, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [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(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(54, 22, F5, 3) (dual of [22, 18, 4]-code or 22-cap in PG(3,5)), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(5131, 15647, F5, 27) (dual of [15647, 15516, 28]-code), using
(104, 104+27, large)-Net in Base 5 — Upper bound on s
There is no (104, 131, large)-net in base 5, because
- 25 times m-reduction [i] would yield (104, 106, large)-net in base 5, but