Best Known (104−20, 104, s)-Nets in Base 32
(104−20, 104, 838860)-Net over F32 — Constructive and digital
Digital (84, 104, 838860)-net over F32, using
- 323 times duplication [i] based on digital (81, 101, 838860)-net over F32, using
- t-expansion [i] based on digital (80, 101, 838860)-net over F32, using
- net defined by OOA [i] based on linear OOA(32101, 838860, F32, 21, 21) (dual of [(838860, 21), 17615959, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(32101, 8388601, F32, 21) (dual of [8388601, 8388500, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(32101, large, F32, 21) (dual of [large, large−101, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(32101, large, F32, 21) (dual of [large, large−101, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(32101, 8388601, F32, 21) (dual of [8388601, 8388500, 22]-code), using
- net defined by OOA [i] based on linear OOA(32101, 838860, F32, 21, 21) (dual of [(838860, 21), 17615959, 22]-NRT-code), using
- t-expansion [i] based on digital (80, 101, 838860)-net over F32, using
(104−20, 104, 838904)-Net in Base 32 — Constructive
(84, 104, 838904)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- (73, 93, 838860)-net in base 32, using
- net defined by OOA [i] based on OOA(3293, 838860, S32, 20, 20), using
- OA 10-folding and stacking [i] based on OA(3293, 8388600, S32, 20), using
- discarding factors based on OA(3293, large, S32, 20), using
- discarding parts of the base [i] based on linear OA(6477, large, F64, 20) (dual of [large, large−77, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding parts of the base [i] based on linear OA(6477, large, F64, 20) (dual of [large, large−77, 21]-code), using
- discarding factors based on OA(3293, large, S32, 20), using
- OA 10-folding and stacking [i] based on OA(3293, 8388600, S32, 20), using
- net defined by OOA [i] based on OOA(3293, 838860, S32, 20, 20), using
- digital (1, 11, 44)-net over F32, using
(104−20, 104, large)-Net over F32 — Digital
Digital (84, 104, large)-net over F32, using
- t-expansion [i] based on digital (83, 104, large)-net over F32, using
- 1 times m-reduction [i] based on digital (83, 105, large)-net over F32, using
(104−20, 104, large)-Net in Base 32 — Upper bound on s
There is no (84, 104, large)-net in base 32, because
- 18 times m-reduction [i] would yield (84, 86, large)-net in base 32, but