Best Known (88−25, 88, s)-Nets in Base 32
(88−25, 88, 2794)-Net over F32 — Constructive and digital
Digital (63, 88, 2794)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-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 (3, 15, 64)-net over F32, using
(88−25, 88, 21845)-Net in Base 32 — Constructive
(63, 88, 21845)-net in base 32, using
- net defined by OOA [i] based on OOA(3288, 21845, S32, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(3288, 262141, S32, 25), using
- discarding factors based on OA(3288, 262147, S32, 25), using
- discarding parts of the base [i] based on linear OA(6473, 262147, F64, 25) (dual of [262147, 262074, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- discarding parts of the base [i] based on linear OA(6473, 262147, F64, 25) (dual of [262147, 262074, 26]-code), using
- discarding factors based on OA(3288, 262147, S32, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(3288, 262141, S32, 25), using
(88−25, 88, 104456)-Net over F32 — Digital
Digital (63, 88, 104456)-net over F32, using
(88−25, 88, large)-Net in Base 32 — Upper bound on s
There is no (63, 88, large)-net in base 32, because
- 23 times m-reduction [i] would yield (63, 65, large)-net in base 32, but