Best Known (113−19, 113, s)-Nets in Base 9
(113−19, 113, 531441)-Net over F9 — Constructive and digital
Digital (94, 113, 531441)-net over F9, using
- net defined by OOA [i] based on linear OOA(9113, 531441, F9, 19, 19) (dual of [(531441, 19), 10097266, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using
(113−19, 113, 2391485)-Net over F9 — Digital
Digital (94, 113, 2391485)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(9113, 2391485, F9, 2, 19) (dual of [(2391485, 2), 4782857, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 2-folding [i] based on linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using
(113−19, 113, large)-Net in Base 9 — Upper bound on s
There is no (94, 113, large)-net in base 9, because
- 17 times m-reduction [i] would yield (94, 96, large)-net in base 9, but