Best Known (108−23, 108, s)-Nets in Base 32
(108−23, 108, 95424)-Net over F32 — Constructive and digital
Digital (85, 108, 95424)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (8, 19, 99)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 3, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (0, 5, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 11, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 3, 33)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (66, 89, 95325)-net over F32, using
- net defined by OOA [i] based on linear OOA(3289, 95325, F32, 23, 23) (dual of [(95325, 23), 2192386, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- OOA 11-folding and stacking with additional row [i] based on linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using
- net defined by OOA [i] based on linear OOA(3289, 95325, F32, 23, 23) (dual of [(95325, 23), 2192386, 24]-NRT-code), using
- digital (8, 19, 99)-net over F32, using
(108−23, 108, 762600)-Net in Base 32 — Constructive
(85, 108, 762600)-net in base 32, using
- base change [i] based on digital (67, 90, 762600)-net over F64, using
- 641 times duplication [i] based on digital (66, 89, 762600)-net over F64, using
- net defined by OOA [i] based on linear OOA(6489, 762600, F64, 23, 23) (dual of [(762600, 23), 17539711, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(6489, 8388601, F64, 23) (dual of [8388601, 8388512, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(6489, large, F64, 23) (dual of [large, large−89, 24]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6489, large, F64, 23) (dual of [large, large−89, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(6489, 8388601, F64, 23) (dual of [8388601, 8388512, 24]-code), using
- net defined by OOA [i] based on linear OOA(6489, 762600, F64, 23, 23) (dual of [(762600, 23), 17539711, 24]-NRT-code), using
- 641 times duplication [i] based on digital (66, 89, 762600)-net over F64, using
(108−23, 108, 7151713)-Net over F32 — Digital
Digital (85, 108, 7151713)-net over F32, using
(108−23, 108, large)-Net in Base 32 — Upper bound on s
There is no (85, 108, large)-net in base 32, because
- 21 times m-reduction [i] would yield (85, 87, large)-net in base 32, but