Best Known (45−7, 45, s)-Nets in Base 7
(45−7, 45, 274521)-Net over F7 — Constructive and digital
Digital (38, 45, 274521)-net over F7, using
- net defined by OOA [i] based on linear OOA(745, 274521, F7, 9, 7) (dual of [(274521, 9), 2470644, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(745, 274522, F7, 3, 7) (dual of [(274522, 3), 823521, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(73, 8, F7, 3, 3) (dual of [(8, 3), 21, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;21,7) [i]
- linear OOA(742, 274514, F7, 3, 7) (dual of [(274514, 3), 823500, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(742, 823542, F7, 7) (dual of [823542, 823500, 8]-code), using
- the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OOA 3-folding [i] based on linear OA(742, 823542, F7, 7) (dual of [823542, 823500, 8]-code), using
- linear OOA(73, 8, F7, 3, 3) (dual of [(8, 3), 21, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(745, 274522, F7, 3, 7) (dual of [(274522, 3), 823521, 8]-NRT-code), using
(45−7, 45, 1087195)-Net over F7 — Digital
Digital (38, 45, 1087195)-net over F7, using
(45−7, 45, large)-Net in Base 7 — Upper bound on s
There is no (38, 45, large)-net in base 7, because
- 5 times m-reduction [i] would yield (38, 40, large)-net in base 7, but