Best Known (60, 60+16, s)-Nets in Base 5
(60, 60+16, 1955)-Net over F5 — Constructive and digital
Digital (60, 76, 1955)-net over F5, using
- net defined by OOA [i] based on linear OOA(576, 1955, F5, 16, 16) (dual of [(1955, 16), 31204, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(576, 15640, F5, 16) (dual of [15640, 15564, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(573, 15625, F5, 16) (dual of [15625, 15552, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(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(15) ⊂ Ce(12) [i] based on
- OA 8-folding and stacking [i] based on linear OA(576, 15640, F5, 16) (dual of [15640, 15564, 17]-code), using
(60, 60+16, 8383)-Net over F5 — Digital
Digital (60, 76, 8383)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(576, 8383, F5, 16) (dual of [8383, 8307, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(576, 15640, F5, 16) (dual of [15640, 15564, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(573, 15625, F5, 16) (dual of [15625, 15552, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(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(15) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(576, 15640, F5, 16) (dual of [15640, 15564, 17]-code), using
(60, 60+16, 4110025)-Net in Base 5 — Upper bound on s
There is no (60, 76, 4110026)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 132348 983589 260214 805289 126377 341708 876793 879648 381825 > 576 [i]