Best Known (53, 53+10, s)-Nets in Base 5
(53, 53+10, 15646)-Net over F5 — Constructive and digital
Digital (53, 63, 15646)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 21)-net over F5, using
- digital (46, 56, 15625)-net over F5, using
- net defined by OOA [i] based on linear OOA(556, 15625, F5, 10, 10) (dual of [(15625, 10), 156194, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(556, 78125, F5, 10) (dual of [78125, 78069, 11]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(557, 78126, F5, 11) (dual of [78126, 78069, 12]-code), using
- OA 5-folding and stacking [i] based on linear OA(556, 78125, F5, 10) (dual of [78125, 78069, 11]-code), using
- net defined by OOA [i] based on linear OOA(556, 15625, F5, 10, 10) (dual of [(15625, 10), 156194, 11]-NRT-code), using
(53, 53+10, 81004)-Net over F5 — Digital
Digital (53, 63, 81004)-net over F5, using
(53, 53+10, large)-Net in Base 5 — Upper bound on s
There is no (53, 63, large)-net in base 5, because
- 8 times m-reduction [i] would yield (53, 55, large)-net in base 5, but