Best Known (73−11, 73, s)-Nets in Base 5
(73−11, 73, 390625)-Net over F5 — Constructive and digital
Digital (62, 73, 390625)-net over F5, using
- net defined by OOA [i] based on linear OOA(573, 390625, F5, 11, 11) (dual of [(390625, 11), 4296802, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(573, 1953126, F5, 11) (dual of [1953126, 1953053, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, 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(573, 1953126, F5, 11) (dual of [1953126, 1953053, 12]-code), using
(73−11, 73, 976563)-Net over F5 — Digital
Digital (62, 73, 976563)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(573, 976563, F5, 2, 11) (dual of [(976563, 2), 1953053, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(573, 1953126, F5, 11) (dual of [1953126, 1953053, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, 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(573, 1953126, F5, 11) (dual of [1953126, 1953053, 12]-code), using
(73−11, 73, large)-Net in Base 5 — Upper bound on s
There is no (62, 73, large)-net in base 5, because
- 9 times m-reduction [i] would yield (62, 64, large)-net in base 5, but