Best Known (104−11, 104, s)-Nets in Base 7
(104−11, 104, 3355440)-Net over F7 — Constructive and digital
Digital (93, 104, 3355440)-net over F7, using
- 72 times duplication [i] based on digital (91, 102, 3355440)-net over F7, using
- trace code for nets [i] based on digital (40, 51, 1677720)-net over F49, using
- net defined by OOA [i] based on linear OOA(4951, 1677720, F49, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4951, 8388601, F49, 11) (dual of [8388601, 8388550, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(4951, large, F49, 11) (dual of [large, large−51, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 28247525 | 4910−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4951, large, F49, 11) (dual of [large, large−51, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4951, 8388601, F49, 11) (dual of [8388601, 8388550, 12]-code), using
- net defined by OOA [i] based on linear OOA(4951, 1677720, F49, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- trace code for nets [i] based on digital (40, 51, 1677720)-net over F49, using
(104−11, 104, large)-Net over F7 — Digital
Digital (93, 104, large)-net over F7, using
- t-expansion [i] based on digital (92, 104, large)-net over F7, using
- 2 times m-reduction [i] based on digital (92, 106, large)-net over F7, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(7106, large, F7, 14) (dual of [large, large−106, 15]-code), using
- trace code [i] based on linear OA(4953, 5764801, F49, 14) (dual of [5764801, 5764748, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- trace code [i] based on linear OA(4953, 5764801, F49, 14) (dual of [5764801, 5764748, 15]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(7106, large, F7, 14) (dual of [large, large−106, 15]-code), using
- 2 times m-reduction [i] based on digital (92, 106, large)-net over F7, using
(104−11, 104, large)-Net in Base 7 — Upper bound on s
There is no (93, 104, large)-net in base 7, because
- 9 times m-reduction [i] would yield (93, 95, large)-net in base 7, but