Best Known (37, 46, s)-Nets in Base 32
(37, 46, 2097194)-Net over F32 — Constructive and digital
Digital (37, 46, 2097194)-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 (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 (1, 5, 44)-net over F32, using
(37, 46, 2097646)-Net in Base 32 — Constructive
(37, 46, 2097646)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 496)-net over F32, using
- net defined by OOA [i] based on linear OOA(326, 496, F32, 4, 4) (dual of [(496, 4), 1978, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(326, 992, F32, 4) (dual of [992, 986, 5]-code), using
- 1 times truncation [i] based on linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(326, 992, F32, 4) (dual of [992, 986, 5]-code), using
- net defined by OOA [i] based on linear OOA(326, 496, F32, 4, 4) (dual of [(496, 4), 1978, 5]-NRT-code), 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
- digital (2, 6, 496)-net over F32, using
(37, 46, large)-Net over F32 — Digital
Digital (37, 46, large)-net over F32, using
- t-expansion [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
(37, 46, large)-Net in Base 32 — Upper bound on s
There is no (37, 46, large)-net in base 32, because
- 7 times m-reduction [i] would yield (37, 39, large)-net in base 32, but