Best Known (79, 79+16, s)-Nets in Base 32
(79, 79+16, 1048864)-Net over F32 — Constructive and digital
Digital (79, 95, 1048864)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 19, 289)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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 (7, 15, 256)-net over F32, using
- net defined by OOA [i] based on linear OOA(3215, 256, F32, 8, 8) (dual of [(256, 8), 2033, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3215, 1024, F32, 8) (dual of [1024, 1009, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(3215, 1024, F32, 8) (dual of [1024, 1009, 9]-code), using
- net defined by OOA [i] based on linear OOA(3215, 256, F32, 8, 8) (dual of [(256, 8), 2033, 9]-NRT-code), using
- digital (0, 4, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (60, 76, 1048575)-net over F32, using
- net defined by OOA [i] based on linear OOA(3276, 1048575, F32, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3276, 8388600, F32, 16) (dual of [8388600, 8388524, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3276, large, F32, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3276, large, F32, 16) (dual of [large, large−76, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3276, 8388600, F32, 16) (dual of [8388600, 8388524, 17]-code), using
- net defined by OOA [i] based on linear OOA(3276, 1048575, F32, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- digital (11, 19, 289)-net over F32, using
(79, 79+16, 1052671)-Net in Base 32 — Constructive
(79, 95, 1052671)-net in base 32, using
- (u, u+v)-construction [i] based on
- (13, 21, 4096)-net in base 32, using
- base change [i] based on digital (7, 15, 4096)-net over F128, using
- net defined by OOA [i] based on linear OOA(12815, 4096, F128, 8, 8) (dual of [(4096, 8), 32753, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(12815, 16384, F128, 8) (dual of [16384, 16369, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(12815, 16384, F128, 8) (dual of [16384, 16369, 9]-code), using
- net defined by OOA [i] based on linear OOA(12815, 4096, F128, 8, 8) (dual of [(4096, 8), 32753, 9]-NRT-code), using
- base change [i] based on digital (7, 15, 4096)-net over F128, using
- (58, 74, 1048575)-net in base 32, using
- net defined by OOA [i] based on OOA(3274, 1048575, S32, 16, 16), using
- OA 8-folding and stacking [i] based on OA(3274, 8388600, S32, 16), using
- discarding factors based on OA(3274, large, S32, 16), using
- discarding parts of the base [i] based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding parts of the base [i] based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- discarding factors based on OA(3274, large, S32, 16), using
- OA 8-folding and stacking [i] based on OA(3274, 8388600, S32, 16), using
- net defined by OOA [i] based on OOA(3274, 1048575, S32, 16, 16), using
- (13, 21, 4096)-net in base 32, using
(79, 79+16, large)-Net over F32 — Digital
Digital (79, 95, large)-net over F32, using
- 5 times m-reduction [i] based on digital (79, 100, large)-net over F32, using
(79, 79+16, large)-Net in Base 32 — Upper bound on s
There is no (79, 95, large)-net in base 32, because
- 14 times m-reduction [i] would yield (79, 81, large)-net in base 32, but