Best Known (36, 45, s)-Nets in Base 32
(36, 45, 2097183)-Net over F32 — Constructive and digital
Digital (36, 45, 2097183)-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 (32, 41, 2097150)-net over F32, using
- net defined by OOA [i] based on linear OOA(3241, 2097150, F32, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3241, 8388601, F32, 9) (dual of [8388601, 8388560, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3241, 8388601, F32, 9) (dual of [8388601, 8388560, 10]-code), using
- net defined by OOA [i] based on linear OOA(3241, 2097150, F32, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
- digital (0, 4, 33)-net over F32, using
(36, 45, 2097215)-Net in Base 32 — Constructive
(36, 45, 2097215)-net in base 32, using
- (u, u+v)-construction [i] based on
- (1, 5, 65)-net in base 32, using
- 1 times m-reduction [i] based on (1, 6, 65)-net in base 32, using
- base change [i] based on digital (0, 5, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- base change [i] based on digital (0, 5, 65)-net over F64, using
- 1 times m-reduction [i] based on (1, 6, 65)-net in base 32, using
- (31, 40, 2097150)-net in base 32, using
- base change [i] based on digital (16, 25, 2097150)-net over F256, using
- net defined by OOA [i] based on linear OOA(25625, 2097150, F256, 9, 9) (dual of [(2097150, 9), 18874325, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(25625, 8388601, F256, 9) (dual of [8388601, 8388576, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(25625, 8388601, F256, 9) (dual of [8388601, 8388576, 10]-code), using
- net defined by OOA [i] based on linear OOA(25625, 2097150, F256, 9, 9) (dual of [(2097150, 9), 18874325, 10]-NRT-code), using
- base change [i] based on digital (16, 25, 2097150)-net over F256, using
- (1, 5, 65)-net in base 32, using
(36, 45, large)-Net over F32 — Digital
Digital (36, 45, large)-net over F32, using
- 1 times m-reduction [i] based on digital (36, 46, large)-net over F32, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3246, large, F32, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3246, large, F32, 10) (dual of [large, large−46, 11]-code), using
(36, 45, large)-Net in Base 32 — Upper bound on s
There is no (36, 45, large)-net in base 32, because
- 7 times m-reduction [i] would yield (36, 38, large)-net in base 32, but