Best Known (90, 113, s)-Nets in Base 5
(90, 113, 1422)-Net over F5 — Constructive and digital
Digital (90, 113, 1422)-net over F5, using
- net defined by OOA [i] based on linear OOA(5113, 1422, F5, 23, 23) (dual of [(1422, 23), 32593, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5113, 15643, F5, 23) (dual of [15643, 15530, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(5113, 15647, F5, 23) (dual of [15647, 15534, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- 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(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(22) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(5113, 15647, F5, 23) (dual of [15647, 15534, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5113, 15643, F5, 23) (dual of [15643, 15530, 24]-code), using
(90, 113, 11580)-Net over F5 — Digital
Digital (90, 113, 11580)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5113, 11580, F5, 23) (dual of [11580, 11467, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(5113, 15647, F5, 23) (dual of [15647, 15534, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- 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(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(22) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(5113, 15647, F5, 23) (dual of [15647, 15534, 24]-code), using
(90, 113, large)-Net in Base 5 — Upper bound on s
There is no (90, 113, large)-net in base 5, because
- 21 times m-reduction [i] would yield (90, 92, large)-net in base 5, but