Best Known (92, 113, s)-Nets in Base 5
(92, 113, 7812)-Net over F5 — Constructive and digital
Digital (92, 113, 7812)-net over F5, using
- net defined by OOA [i] based on linear OOA(5113, 7812, F5, 21, 21) (dual of [(7812, 21), 163939, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(5113, 78121, F5, 21) (dual of [78121, 78008, 22]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(5113, 78121, F5, 21) (dual of [78121, 78008, 22]-code), using
(92, 113, 38570)-Net over F5 — Digital
Digital (92, 113, 38570)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5113, 38570, F5, 2, 21) (dual of [(38570, 2), 77027, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5113, 39063, F5, 2, 21) (dual of [(39063, 2), 78013, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5113, 78126, F5, 21) (dual of [78126, 78013, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- OOA 2-folding [i] based on linear OA(5113, 78126, F5, 21) (dual of [78126, 78013, 22]-code), using
- discarding factors / shortening the dual code based on linear OOA(5113, 39063, F5, 2, 21) (dual of [(39063, 2), 78013, 22]-NRT-code), using
(92, 113, large)-Net in Base 5 — Upper bound on s
There is no (92, 113, large)-net in base 5, because
- 19 times m-reduction [i] would yield (92, 94, large)-net in base 5, but