Best Known (94−25, 94, s)-Nets in Base 32
(94−25, 94, 2834)-Net over F32 — Constructive and digital
Digital (69, 94, 2834)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (9, 21, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (48, 73, 2730)-net over F32, using
- net defined by OOA [i] based on linear OOA(3273, 2730, F32, 25, 25) (dual of [(2730, 25), 68177, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3273, 32761, F32, 25) (dual of [32761, 32688, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3273, 32768, F32, 25) (dual of [32768, 32695, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(3273, 32768, F32, 25) (dual of [32768, 32695, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3273, 32761, F32, 25) (dual of [32761, 32688, 26]-code), using
- net defined by OOA [i] based on linear OOA(3273, 2730, F32, 25, 25) (dual of [(2730, 25), 68177, 26]-NRT-code), using
- digital (9, 21, 104)-net over F32, using
(94−25, 94, 21847)-Net in Base 32 — Constructive
(69, 94, 21847)-net in base 32, using
- net defined by OOA [i] based on OOA(3294, 21847, S32, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(3294, 262165, S32, 25), using
- discarding factors based on OA(3294, 262168, S32, 25), using
- discarding parts of the base [i] based on linear OA(6478, 262168, F64, 25) (dual of [262168, 262090, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(6473, 262145, F64, 25) (dual of [262145, 262072, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(6455, 262145, F64, 19) (dual of [262145, 262090, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(645, 23, F64, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- discarding parts of the base [i] based on linear OA(6478, 262168, F64, 25) (dual of [262168, 262090, 26]-code), using
- discarding factors based on OA(3294, 262168, S32, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(3294, 262165, S32, 25), using
(94−25, 94, 248424)-Net over F32 — Digital
Digital (69, 94, 248424)-net over F32, using
(94−25, 94, large)-Net in Base 32 — Upper bound on s
There is no (69, 94, large)-net in base 32, because
- 23 times m-reduction [i] would yield (69, 71, large)-net in base 32, but