Best Known (108−22, 108, s)-Nets in Base 5
(108−22, 108, 1422)-Net over F5 — Constructive and digital
Digital (86, 108, 1422)-net over F5, using
- 51 times duplication [i] based on digital (85, 107, 1422)-net over F5, using
- net defined by OOA [i] based on linear OOA(5107, 1422, F5, 22, 22) (dual of [(1422, 22), 31177, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(5107, 15642, F5, 22) (dual of [15642, 15535, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(5107, 15647, F5, 22) (dual of [15647, 15540, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- 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(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5107, 15647, F5, 22) (dual of [15647, 15540, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(5107, 15642, F5, 22) (dual of [15642, 15535, 23]-code), using
- net defined by OOA [i] based on linear OOA(5107, 1422, F5, 22, 22) (dual of [(1422, 22), 31177, 23]-NRT-code), using
(108−22, 108, 11382)-Net over F5 — Digital
Digital (86, 108, 11382)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5108, 11382, F5, 22) (dual of [11382, 11274, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(5108, 15649, F5, 22) (dual of [15649, 15541, 23]-code), using
- construction XX applied to Ce(21) ⊂ Ce(17) ⊂ Ce(16) [i] based on
- 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(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(579, 15625, F5, 17) (dual of [15625, 15546, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(5108, 15649, F5, 22) (dual of [15649, 15541, 23]-code), using
(108−22, 108, large)-Net in Base 5 — Upper bound on s
There is no (86, 108, large)-net in base 5, because
- 20 times m-reduction [i] would yield (86, 88, large)-net in base 5, but