Best Known (69−14, 69, s)-Nets in Base 7
(69−14, 69, 2414)-Net over F7 — Constructive and digital
Digital (55, 69, 2414)-net over F7, using
- t-expansion [i] based on digital (54, 69, 2414)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 13)-net over F7, using
- 5 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- digital (46, 61, 2401)-net over F7, using
- net defined by OOA [i] based on linear OOA(761, 2401, F7, 15, 15) (dual of [(2401, 15), 35954, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(761, 16808, F7, 15) (dual of [16808, 16747, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(761, 16808, F7, 15) (dual of [16808, 16747, 16]-code), using
- net defined by OOA [i] based on linear OOA(761, 2401, F7, 15, 15) (dual of [(2401, 15), 35954, 16]-NRT-code), using
- digital (1, 8, 13)-net over F7, using
- (u, u+v)-construction [i] based on
(69−14, 69, 28898)-Net over F7 — Digital
Digital (55, 69, 28898)-net over F7, using
(69−14, 69, large)-Net in Base 7 — Upper bound on s
There is no (55, 69, large)-net in base 7, because
- 12 times m-reduction [i] would yield (55, 57, large)-net in base 7, but