Best Known (139−29, 139, s)-Nets in Base 5
(139−29, 139, 1116)-Net over F5 — Constructive and digital
Digital (110, 139, 1116)-net over F5, using
- net defined by OOA [i] based on linear OOA(5139, 1116, F5, 29, 29) (dual of [(1116, 29), 32225, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(5139, 15625, F5, 29) (dual of [15625, 15486, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- OOA 14-folding and stacking with additional row [i] based on linear OA(5139, 15625, F5, 29) (dual of [15625, 15486, 30]-code), using
(139−29, 139, 10187)-Net over F5 — Digital
Digital (110, 139, 10187)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5139, 10187, F5, 29) (dual of [10187, 10048, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(5139, 15625, F5, 29) (dual of [15625, 15486, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(5139, 15625, F5, 29) (dual of [15625, 15486, 30]-code), using
(139−29, 139, large)-Net in Base 5 — Upper bound on s
There is no (110, 139, large)-net in base 5, because
- 27 times m-reduction [i] would yield (110, 112, large)-net in base 5, but