Best Known (93−26, 93, s)-Nets in Base 32
(93−26, 93, 2585)-Net over F32 — Constructive and digital
Digital (67, 93, 2585)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 16, 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 (51, 77, 2521)-net over F32, using
- net defined by OOA [i] based on linear OOA(3277, 2521, F32, 26, 26) (dual of [(2521, 26), 65469, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3277, 32773, F32, 26) (dual of [32773, 32696, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3277, 32775, F32, 26) (dual of [32775, 32698, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- linear OA(3276, 32768, F32, 26) (dual of [32768, 32692, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3270, 32768, F32, 24) (dual of [32768, 32698, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(3277, 32775, F32, 26) (dual of [32775, 32698, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3277, 32773, F32, 26) (dual of [32773, 32696, 27]-code), using
- net defined by OOA [i] based on linear OOA(3277, 2521, F32, 26, 26) (dual of [(2521, 26), 65469, 27]-NRT-code), using
- digital (3, 16, 64)-net over F32, using
(93−26, 93, 20165)-Net in Base 32 — Constructive
(67, 93, 20165)-net in base 32, using
- 321 times duplication [i] based on (66, 92, 20165)-net in base 32, using
- net defined by OOA [i] based on OOA(3292, 20165, S32, 26, 26), using
- OA 13-folding and stacking [i] based on OA(3292, 262145, S32, 26), using
- discarding factors based on OA(3292, 262147, S32, 26), using
- discarding parts of the base [i] based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 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(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(25) ⊂ Ce(24) [i] based on
- discarding parts of the base [i] based on linear OA(6476, 262147, F64, 26) (dual of [262147, 262071, 27]-code), using
- discarding factors based on OA(3292, 262147, S32, 26), using
- OA 13-folding and stacking [i] based on OA(3292, 262145, S32, 26), using
- net defined by OOA [i] based on OOA(3292, 20165, S32, 26, 26), using
(93−26, 93, 130456)-Net over F32 — Digital
Digital (67, 93, 130456)-net over F32, using
(93−26, 93, large)-Net in Base 32 — Upper bound on s
There is no (67, 93, large)-net in base 32, because
- 24 times m-reduction [i] would yield (67, 69, large)-net in base 32, but