Best Known (68, 68+27, s)-Nets in Base 32
(68, 68+27, 2584)-Net over F32 — Constructive and digital
Digital (68, 95, 2584)-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 (52, 79, 2520)-net over F32, using
- net defined by OOA [i] based on linear OOA(3279, 2520, F32, 27, 27) (dual of [(2520, 27), 67961, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3279, 32761, F32, 27) (dual of [32761, 32682, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3279, 32768, F32, 27) (dual of [32768, 32689, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(3279, 32768, F32, 27) (dual of [32768, 32689, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3279, 32761, F32, 27) (dual of [32761, 32682, 28]-code), using
- net defined by OOA [i] based on linear OOA(3279, 2520, F32, 27, 27) (dual of [(2520, 27), 67961, 28]-NRT-code), using
- digital (3, 16, 64)-net over F32, using
(68, 68+27, 20165)-Net in Base 32 — Constructive
(68, 95, 20165)-net in base 32, using
- net defined by OOA [i] based on OOA(3295, 20165, S32, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(3295, 262146, S32, 27), using
- discarding factors based on OA(3295, 262147, S32, 27), using
- discarding parts of the base [i] based on linear OA(6479, 262147, F64, 27) (dual of [262147, 262068, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(6479, 262144, F64, 27) (dual of [262144, 262065, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(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(26) ⊂ Ce(25) [i] based on
- discarding parts of the base [i] based on linear OA(6479, 262147, F64, 27) (dual of [262147, 262068, 28]-code), using
- discarding factors based on OA(3295, 262147, S32, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(3295, 262146, S32, 27), using
(68, 68+27, 107540)-Net over F32 — Digital
Digital (68, 95, 107540)-net over F32, using
(68, 68+27, large)-Net in Base 32 — Upper bound on s
There is no (68, 95, large)-net in base 32, because
- 25 times m-reduction [i] would yield (68, 70, large)-net in base 32, but