Best Known (46, 46+11, s)-Nets in Base 5
(46, 46+11, 15625)-Net over F5 — Constructive and digital
Digital (46, 57, 15625)-net over F5, using
- net defined by OOA [i] based on linear OOA(557, 15625, F5, 11, 11) (dual of [(15625, 11), 171818, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(557, 78126, F5, 11) (dual of [78126, 78069, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(557, 78126, F5, 11) (dual of [78126, 78069, 12]-code), using
(46, 46+11, 39063)-Net over F5 — Digital
Digital (46, 57, 39063)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(557, 39063, F5, 2, 11) (dual of [(39063, 2), 78069, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(557, 78126, F5, 11) (dual of [78126, 78069, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 2-folding [i] based on linear OA(557, 78126, F5, 11) (dual of [78126, 78069, 12]-code), using
(46, 46+11, large)-Net in Base 5 — Upper bound on s
There is no (46, 57, large)-net in base 5, because
- 9 times m-reduction [i] would yield (46, 48, large)-net in base 5, but