Best Known (96−17, 96, s)-Nets in Base 7
(96−17, 96, 14720)-Net over F7 — Constructive and digital
Digital (79, 96, 14720)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 14)-net over F7, using
- 3 times m-reduction [i] based on digital (3, 14, 14)-net over F7, using
- digital (68, 85, 14706)-net over F7, using
- net defined by OOA [i] based on linear OOA(785, 14706, F7, 17, 17) (dual of [(14706, 17), 249917, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(785, 117649, F7, 17) (dual of [117649, 117564, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(785, 117649, F7, 17) (dual of [117649, 117564, 18]-code), using
- net defined by OOA [i] based on linear OOA(785, 14706, F7, 17, 17) (dual of [(14706, 17), 249917, 18]-NRT-code), using
- digital (3, 11, 14)-net over F7, using
(96−17, 96, 133353)-Net over F7 — Digital
Digital (79, 96, 133353)-net over F7, using
(96−17, 96, large)-Net in Base 7 — Upper bound on s
There is no (79, 96, large)-net in base 7, because
- 15 times m-reduction [i] would yield (79, 81, large)-net in base 7, but