Best Known (70, 70+19, s)-Nets in Base 7
(70, 70+19, 1871)-Net over F7 — Constructive and digital
Digital (70, 89, 1871)-net over F7, using
- net defined by OOA [i] based on linear OOA(789, 1871, F7, 19, 19) (dual of [(1871, 19), 35460, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(789, 16840, F7, 19) (dual of [16840, 16751, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(788, 16839, F7, 19) (dual of [16839, 16751, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(781, 16807, F7, 19) (dual of [16807, 16726, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(77, 32, F7, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(788, 16839, F7, 19) (dual of [16839, 16751, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(789, 16840, F7, 19) (dual of [16840, 16751, 20]-code), using
(70, 70+19, 18999)-Net over F7 — Digital
Digital (70, 89, 18999)-net over F7, using
(70, 70+19, large)-Net in Base 7 — Upper bound on s
There is no (70, 89, large)-net in base 7, because
- 17 times m-reduction [i] would yield (70, 72, large)-net in base 7, but