Best Known (46, 61, s)-Nets in Base 7
(46, 61, 2401)-Net over F7 — Constructive and digital
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
(46, 61, 8404)-Net over F7 — Digital
Digital (46, 61, 8404)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(761, 8404, F7, 2, 15) (dual of [(8404, 2), 16747, 16]-NRT-code), using
- OOA 2-folding [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 2-folding [i] based on linear OA(761, 16808, F7, 15) (dual of [16808, 16747, 16]-code), using
(46, 61, large)-Net in Base 7 — Upper bound on s
There is no (46, 61, large)-net in base 7, because
- 13 times m-reduction [i] would yield (46, 48, large)-net in base 7, but