Best Known (88, 88+11, s)-Nets in Base 7
(88, 88+11, 2308329)-Net over F7 — Constructive and digital
Digital (88, 99, 2308329)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (12, 17, 2409)-net over F7, using
- net defined by OOA [i] based on linear OOA(717, 2409, F7, 6, 5) (dual of [(2409, 6), 14437, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(717, 2410, F7, 2, 5) (dual of [(2410, 2), 4803, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(73, 57, F7, 2, 2) (dual of [(57, 2), 111, 3]-NRT-code), using
- appending kth column [i] based on linear OA(73, 57, F7, 2) (dual of [57, 54, 3]-code), using
- Hamming code H(3,7) [i]
- appending kth column [i] based on linear OA(73, 57, F7, 2) (dual of [57, 54, 3]-code), using
- linear OOA(714, 2353, F7, 2, 5) (dual of [(2353, 2), 4692, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(714, 4706, F7, 5) (dual of [4706, 4692, 6]-code), using
- trace code [i] based on linear OA(497, 2353, F49, 5) (dual of [2353, 2346, 6]-code), using
- OOA 2-folding [i] based on linear OA(714, 4706, F7, 5) (dual of [4706, 4692, 6]-code), using
- linear OOA(73, 57, F7, 2, 2) (dual of [(57, 2), 111, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(717, 2410, F7, 2, 5) (dual of [(2410, 2), 4803, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(717, 2409, F7, 6, 5) (dual of [(2409, 6), 14437, 6]-NRT-code), using
- digital (71, 82, 2305920)-net over F7, using
- trace code for nets [i] based on digital (30, 41, 1152960)-net over F49, using
- net defined by OOA [i] based on linear OOA(4941, 1152960, F49, 11, 11) (dual of [(1152960, 11), 12682519, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4941, 5764801, F49, 11) (dual of [5764801, 5764760, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(4941, 5764801, F49, 11) (dual of [5764801, 5764760, 12]-code), using
- net defined by OOA [i] based on linear OOA(4941, 1152960, F49, 11, 11) (dual of [(1152960, 11), 12682519, 12]-NRT-code), using
- trace code for nets [i] based on digital (30, 41, 1152960)-net over F49, using
- digital (12, 17, 2409)-net over F7, using
(88, 88+11, large)-Net over F7 — Digital
Digital (88, 99, large)-net over F7, using
- 71 times duplication [i] based on digital (87, 98, large)-net over F7, using
- t-expansion [i] based on digital (85, 98, large)-net over F7, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(798, large, F7, 13) (dual of [large, large−98, 14]-code), using
- trace code [i] based on linear OA(4949, 5764802, F49, 13) (dual of [5764802, 5764753, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- trace code [i] based on linear OA(4949, 5764802, F49, 13) (dual of [5764802, 5764753, 14]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(798, large, F7, 13) (dual of [large, large−98, 14]-code), using
- t-expansion [i] based on digital (85, 98, large)-net over F7, using
(88, 88+11, large)-Net in Base 7 — Upper bound on s
There is no (88, 99, large)-net in base 7, because
- 9 times m-reduction [i] would yield (88, 90, large)-net in base 7, but