Best Known (116−21, 116, s)-Nets in Base 5
(116−21, 116, 7814)-Net over F5 — Constructive and digital
Digital (95, 116, 7814)-net over F5, using
- net defined by OOA [i] based on linear OOA(5116, 7814, F5, 21, 21) (dual of [(7814, 21), 163978, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(5116, 78141, F5, 21) (dual of [78141, 78025, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(5116, 78142, F5, 21) (dual of [78142, 78026, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(53, 17, F5, 2) (dual of [17, 14, 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(20) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5116, 78142, F5, 21) (dual of [78142, 78026, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(5116, 78141, F5, 21) (dual of [78141, 78025, 22]-code), using
(116−21, 116, 39071)-Net over F5 — Digital
Digital (95, 116, 39071)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5116, 39071, F5, 2, 21) (dual of [(39071, 2), 78026, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5116, 78142, F5, 21) (dual of [78142, 78026, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(53, 17, F5, 2) (dual of [17, 14, 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(20) ⊂ Ce(17) [i] based on
- OOA 2-folding [i] based on linear OA(5116, 78142, F5, 21) (dual of [78142, 78026, 22]-code), using
(116−21, 116, large)-Net in Base 5 — Upper bound on s
There is no (95, 116, large)-net in base 5, because
- 19 times m-reduction [i] would yield (95, 97, large)-net in base 5, but