Best Known (66, 66+17, s)-Nets in Base 5
(66, 66+17, 1955)-Net over F5 — Constructive and digital
Digital (66, 83, 1955)-net over F5, using
- net defined by OOA [i] based on linear OOA(583, 1955, F5, 17, 17) (dual of [(1955, 17), 33152, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(583, 15641, F5, 17) (dual of [15641, 15558, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(583, 15647, F5, 17) (dual of [15647, 15564, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- 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(561, 15625, F5, 13) (dual of [15625, 15564, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(16) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(583, 15647, F5, 17) (dual of [15647, 15564, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(583, 15641, F5, 17) (dual of [15641, 15558, 18]-code), using
(66, 66+17, 10625)-Net over F5 — Digital
Digital (66, 83, 10625)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(583, 10625, F5, 17) (dual of [10625, 10542, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(583, 15647, F5, 17) (dual of [15647, 15564, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- 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(561, 15625, F5, 13) (dual of [15625, 15564, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(16) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(583, 15647, F5, 17) (dual of [15647, 15564, 18]-code), using
(66, 66+17, large)-Net in Base 5 — Upper bound on s
There is no (66, 83, large)-net in base 5, because
- 15 times m-reduction [i] would yield (66, 68, large)-net in base 5, but