Best Known (108−17, 108, s)-Nets in Base 32
(108−17, 108, 1056811)-Net over F32 — Constructive and digital
Digital (91, 108, 1056811)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (19, 27, 8236)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 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 (14, 22, 8192)-net over F32, using
- net defined by OOA [i] based on linear OOA(3222, 8192, F32, 8, 8) (dual of [(8192, 8), 65514, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using
- net defined by OOA [i] based on linear OOA(3222, 8192, F32, 8, 8) (dual of [(8192, 8), 65514, 9]-NRT-code), using
- digital (1, 5, 44)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (64, 81, 1048575)-net over F32, using
- net defined by OOA [i] based on linear OOA(3281, 1048575, F32, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3281, 8388601, F32, 17) (dual of [8388601, 8388520, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3281, large, F32, 17) (dual of [large, large−81, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3281, large, F32, 17) (dual of [large, large−81, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3281, 8388601, F32, 17) (dual of [8388601, 8388520, 18]-code), using
- net defined by OOA [i] based on linear OOA(3281, 1048575, F32, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
- digital (19, 27, 8236)-net over F32, using
(108−17, 108, 1310721)-Net in Base 32 — Constructive
(91, 108, 1310721)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (22, 30, 262146)-net over F32, using
- net defined by OOA [i] based on linear OOA(3230, 262146, F32, 8, 8) (dual of [(262146, 8), 2097138, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3230, 1048584, F32, 8) (dual of [1048584, 1048554, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3230, 1048585, F32, 8) (dual of [1048585, 1048555, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(3229, 1048576, F32, 8) (dual of [1048576, 1048547, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(321, 9, F32, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(3230, 1048585, F32, 8) (dual of [1048585, 1048555, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(3230, 1048584, F32, 8) (dual of [1048584, 1048554, 9]-code), using
- net defined by OOA [i] based on linear OOA(3230, 262146, F32, 8, 8) (dual of [(262146, 8), 2097138, 9]-NRT-code), using
- (61, 78, 1048575)-net in base 32, using
- base change [i] based on digital (48, 65, 1048575)-net over F64, using
- net defined by OOA [i] based on linear OOA(6465, 1048575, F64, 17, 17) (dual of [(1048575, 17), 17825710, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(6465, 8388601, F64, 17) (dual of [8388601, 8388536, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(6465, 8388601, F64, 17) (dual of [8388601, 8388536, 18]-code), using
- net defined by OOA [i] based on linear OOA(6465, 1048575, F64, 17, 17) (dual of [(1048575, 17), 17825710, 18]-NRT-code), using
- base change [i] based on digital (48, 65, 1048575)-net over F64, using
- digital (22, 30, 262146)-net over F32, using
(108−17, 108, large)-Net over F32 — Digital
Digital (91, 108, large)-net over F32, using
- t-expansion [i] based on digital (87, 108, large)-net over F32, using
- 2 times m-reduction [i] based on digital (87, 110, large)-net over F32, using
(108−17, 108, large)-Net in Base 32 — Upper bound on s
There is no (91, 108, large)-net in base 32, because
- 15 times m-reduction [i] would yield (91, 93, large)-net in base 32, but