Best Known (62, 72, s)-Nets in Base 5
(62, 72, 390625)-Net over F5 — Constructive and digital
Digital (62, 72, 390625)-net over F5, using
- net defined by OOA [i] based on linear OOA(572, 390625, F5, 10, 10) (dual of [(390625, 10), 3906178, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(572, 1953125, F5, 10) (dual of [1953125, 1953053, 11]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(573, 1953126, F5, 11) (dual of [1953126, 1953053, 12]-code), using
- OA 5-folding and stacking [i] based on linear OA(572, 1953125, F5, 10) (dual of [1953125, 1953053, 11]-code), using
(62, 72, 1503098)-Net over F5 — Digital
Digital (62, 72, 1503098)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(572, 1503098, F5, 10) (dual of [1503098, 1503026, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(572, 1953124, F5, 10) (dual of [1953124, 1953052, 11]-code), using
- the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(572, 1953124, F5, 10) (dual of [1953124, 1953052, 11]-code), using
(62, 72, large)-Net in Base 5 — Upper bound on s
There is no (62, 72, large)-net in base 5, because
- 8 times m-reduction [i] would yield (62, 64, large)-net in base 5, but