Best Known (99−15, 99, s)-Nets in Base 32
(99−15, 99, 1547930)-Net over F32 — Constructive and digital
Digital (84, 99, 1547930)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (21, 28, 349559)-net over F32, using
- (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 (18, 25, 349526)-net over F32, using
- net defined by OOA [i] based on linear OOA(3225, 349526, F32, 7, 7) (dual of [(349526, 7), 2446657, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3225, 1048579, F32, 7) (dual of [1048579, 1048554, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(3225, 1048580, F32, 7) (dual of [1048580, 1048555, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(3225, 1048576, F32, 7) (dual of [1048576, 1048551, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(3221, 1048576, F32, 6) (dual of [1048576, 1048555, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(3225, 1048580, F32, 7) (dual of [1048580, 1048555, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3225, 1048579, F32, 7) (dual of [1048579, 1048554, 8]-code), using
- net defined by OOA [i] based on linear OOA(3225, 349526, F32, 7, 7) (dual of [(349526, 7), 2446657, 8]-NRT-code), using
- digital (0, 3, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (56, 71, 1198371)-net over F32, using
- net defined by OOA [i] based on linear OOA(3271, 1198371, F32, 15, 15) (dual of [(1198371, 15), 17975494, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3271, 8388598, F32, 15) (dual of [8388598, 8388527, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3271, large, F32, 15) (dual of [large, large−71, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3271, large, F32, 15) (dual of [large, large−71, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3271, 8388598, F32, 15) (dual of [8388598, 8388527, 16]-code), using
- net defined by OOA [i] based on linear OOA(3271, 1198371, F32, 15, 15) (dual of [(1198371, 15), 17975494, 16]-NRT-code), using
- digital (21, 28, 349559)-net over F32, using
(99−15, 99, 2396742)-Net in Base 32 — Constructive
(84, 99, 2396742)-net in base 32, using
- (u, u+v)-construction [i] based on
- (23, 30, 2796200)-net in base 32, using
- base change [i] based on digital (18, 25, 2796200)-net over F64, using
- net defined by OOA [i] based on linear OOA(6425, 2796200, F64, 7, 7) (dual of [(2796200, 7), 19573375, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(6425, 8388601, F64, 7) (dual of [8388601, 8388576, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(6425, 8388601, F64, 7) (dual of [8388601, 8388576, 8]-code), using
- net defined by OOA [i] based on linear OOA(6425, 2796200, F64, 7, 7) (dual of [(2796200, 7), 19573375, 8]-NRT-code), using
- base change [i] based on digital (18, 25, 2796200)-net over F64, using
- (54, 69, 1198371)-net in base 32, using
- net defined by OOA [i] based on OOA(3269, 1198371, S32, 15, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(3269, 8388598, S32, 15), using
- discarding factors based on OA(3269, large, S32, 15), using
- discarding parts of the base [i] based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding parts of the base [i] based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- discarding factors based on OA(3269, large, S32, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(3269, 8388598, S32, 15), using
- net defined by OOA [i] based on OOA(3269, 1198371, S32, 15, 15), using
- (23, 30, 2796200)-net in base 32, using
(99−15, 99, large)-Net over F32 — Digital
Digital (84, 99, large)-net over F32, using
- t-expansion [i] based on digital (83, 99, large)-net over F32, using
- 6 times m-reduction [i] based on digital (83, 105, large)-net over F32, using
(99−15, 99, large)-Net in Base 32 — Upper bound on s
There is no (84, 99, large)-net in base 32, because
- 13 times m-reduction [i] would yield (84, 86, large)-net in base 32, but