Best Known (96, 96+16, s)-Nets in Base 5
(96, 96+16, 244143)-Net over F5 — Constructive and digital
Digital (96, 112, 244143)-net over F5, using
- net defined by OOA [i] based on linear OOA(5112, 244143, F5, 16, 16) (dual of [(244143, 16), 3906176, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(5112, 1953144, F5, 16) (dual of [1953144, 1953032, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(5112, 1953146, F5, 16) (dual of [1953146, 1953034, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(591, 1953125, F5, 13) (dual of [1953125, 1953034, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(53, 21, F5, 2) (dual of [21, 18, 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(5112, 1953146, F5, 16) (dual of [1953146, 1953034, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(5112, 1953144, F5, 16) (dual of [1953144, 1953032, 17]-code), using
(96, 96+16, 976573)-Net over F5 — Digital
Digital (96, 112, 976573)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5112, 976573, F5, 2, 16) (dual of [(976573, 2), 1953034, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5112, 1953146, F5, 16) (dual of [1953146, 1953034, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(591, 1953125, F5, 13) (dual of [1953125, 1953034, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(53, 21, F5, 2) (dual of [21, 18, 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
- OOA 2-folding [i] based on linear OA(5112, 1953146, F5, 16) (dual of [1953146, 1953034, 17]-code), using
(96, 96+16, large)-Net in Base 5 — Upper bound on s
There is no (96, 112, large)-net in base 5, because
- 14 times m-reduction [i] would yield (96, 98, large)-net in base 5, but