Best Known (87, 87+20, s)-Nets in Base 32
(87, 87+20, 838904)-Net over F32 — Constructive and digital
Digital (87, 107, 838904)-net over F32, 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
- digital (76, 96, 838860)-net over F32, using
- net defined by OOA [i] based on linear OOA(3296, 838860, F32, 20, 20) (dual of [(838860, 20), 16777104, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3296, 8388600, F32, 20) (dual of [8388600, 8388504, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3296, large, F32, 20) (dual of [large, large−96, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(3296, large, F32, 20) (dual of [large, large−96, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3296, 8388600, F32, 20) (dual of [8388600, 8388504, 21]-code), using
- net defined by OOA [i] based on linear OOA(3296, 838860, F32, 20, 20) (dual of [(838860, 20), 16777104, 21]-NRT-code), using
- digital (1, 11, 44)-net over F32, using
(87, 87+20, 838989)-Net in Base 32 — Constructive
(87, 107, 838989)-net in base 32, using
- (u, u+v)-construction [i] based on
- (4, 14, 129)-net in base 32, using
- base change [i] based on digital (0, 10, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 10, 129)-net over F128, 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
- (4, 14, 129)-net in base 32, using
(87, 87+20, large)-Net over F32 — Digital
Digital (87, 107, large)-net over F32, using
- 3 times m-reduction [i] based on digital (87, 110, large)-net over F32, using
(87, 87+20, large)-Net in Base 32 — Upper bound on s
There is no (87, 107, large)-net in base 32, because
- 18 times m-reduction [i] would yield (87, 89, large)-net in base 32, but