Best Known (88, 88+17, s)-Nets in Base 9
(88, 88+17, 132864)-Net over F9 — Constructive and digital
Digital (88, 105, 132864)-net over F9, using
- 91 times duplication [i] based on digital (87, 104, 132864)-net over F9, using
- net defined by OOA [i] based on linear OOA(9104, 132864, F9, 17, 17) (dual of [(132864, 17), 2258584, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(9104, 1062913, F9, 17) (dual of [1062913, 1062809, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(9104, 1062914, F9, 17) (dual of [1062914, 1062810, 18]-code), using
- trace code [i] based on linear OA(8152, 531457, F81, 17) (dual of [531457, 531405, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(8149, 531442, F81, 17) (dual of [531442, 531393, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(8137, 531442, F81, 13) (dual of [531442, 531405, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(813, 15, F81, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,81) or 15-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- trace code [i] based on linear OA(8152, 531457, F81, 17) (dual of [531457, 531405, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(9104, 1062914, F9, 17) (dual of [1062914, 1062810, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(9104, 1062913, F9, 17) (dual of [1062913, 1062809, 18]-code), using
- net defined by OOA [i] based on linear OOA(9104, 132864, F9, 17, 17) (dual of [(132864, 17), 2258584, 18]-NRT-code), using
(88, 88+17, 1554774)-Net over F9 — Digital
Digital (88, 105, 1554774)-net over F9, using
(88, 88+17, large)-Net in Base 9 — Upper bound on s
There is no (88, 105, large)-net in base 9, because
- 15 times m-reduction [i] would yield (88, 90, large)-net in base 9, but