Best Known (6, 11, s)-Nets in Base 32
(6, 11, 1489)-Net over F32 — Constructive and digital
Digital (6, 11, 1489)-net over F32, using
- net defined by OOA [i] based on linear OOA(3211, 1489, F32, 5, 5) (dual of [(1489, 5), 7434, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3211, 2979, F32, 5) (dual of [2979, 2968, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(321, 993, F32, 1) (dual of [993, 992, 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
- linear OA(323, 993, F32, 2) (dual of [993, 990, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(323, 1023, F32, 2) (dual of [1023, 1020, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(323, 1023, F32, 2) (dual of [1023, 1020, 3]-code), using
- linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- linear OA(321, 993, F32, 1) (dual of [993, 992, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(3211, 2979, F32, 5) (dual of [2979, 2968, 6]-code), using
(6, 11, 2979)-Net over F32 — Digital
Digital (6, 11, 2979)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3211, 2979, F32, 5) (dual of [2979, 2968, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(321, 993, F32, 1) (dual of [993, 992, 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
- linear OA(323, 993, F32, 2) (dual of [993, 990, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(323, 1023, F32, 2) (dual of [1023, 1020, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(323, 1023, F32, 2) (dual of [1023, 1020, 3]-code), using
- linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- linear OA(321, 993, F32, 1) (dual of [993, 992, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
(6, 11, 8128)-Net in Base 32 — Constructive
(6, 11, 8128)-net in base 32, using
- 321 times duplication [i] based on (5, 10, 8128)-net in base 32, using
- net defined by OOA [i] based on OOA(3210, 8128, S32, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(3210, 16257, S32, 5), using
- discarding parts of the base [i] based on linear OA(1287, 16257, F128, 5) (dual of [16257, 16250, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on OA(3210, 16257, S32, 5), using
- net defined by OOA [i] based on OOA(3210, 8128, S32, 5, 5), using
(6, 11, 1530745)-Net in Base 32 — Upper bound on s
There is no (6, 11, 1530746)-net in base 32, because
- 1 times m-reduction [i] would yield (6, 10, 1530746)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1125 900414 015644 > 3210 [i]