Best Known (69, 69+16, s)-Nets in Base 32
(69, 69+16, 1048619)-Net over F32 — Constructive and digital
Digital (69, 85, 1048619)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 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 (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 (1, 9, 44)-net over F32, using
(69, 69+16, 1048655)-Net in Base 32 — Constructive
(69, 85, 1048655)-net in base 32, using
- 321 times duplication [i] based on (68, 84, 1048655)-net in base 32, using
- base change [i] based on digital (54, 70, 1048655)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- digital (45, 61, 1048575)-net over F64, using
- net defined by OOA [i] based on linear OOA(6461, 1048575, F64, 16, 16) (dual of [(1048575, 16), 16777139, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(6461, 8388600, F64, 16) (dual of [8388600, 8388539, 17]-code), using
- discarding factors / shortening the dual code 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 factors / shortening the dual code based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(6461, 8388600, F64, 16) (dual of [8388600, 8388539, 17]-code), using
- net defined by OOA [i] based on linear OOA(6461, 1048575, F64, 16, 16) (dual of [(1048575, 16), 16777139, 17]-NRT-code), using
- digital (1, 9, 80)-net over F64, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (54, 70, 1048655)-net over F64, using
(69, 69+16, large)-Net over F32 — Digital
Digital (69, 85, large)-net over F32, using
- t-expansion [i] based on digital (68, 85, large)-net over F32, using
- 1 times m-reduction [i] based on digital (68, 86, large)-net over F32, using
(69, 69+16, large)-Net in Base 32 — Upper bound on s
There is no (69, 85, large)-net in base 32, because
- 14 times m-reduction [i] would yield (69, 71, large)-net in base 32, but