Best Known (11, 17, s)-Nets in Base 5
(11, 17, 208)-Net over F5 — Constructive and digital
Digital (11, 17, 208)-net over F5, using
- net defined by OOA [i] based on linear OOA(517, 208, F5, 6, 6) (dual of [(208, 6), 1231, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(517, 624, F5, 6) (dual of [624, 607, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(517, 624, F5, 6) (dual of [624, 607, 7]-code), using
(11, 17, 344)-Net over F5 — Digital
Digital (11, 17, 344)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(517, 344, F5, 6) (dual of [344, 327, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(517, 624, F5, 6) (dual of [624, 607, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(517, 624, F5, 6) (dual of [624, 607, 7]-code), using
(11, 17, 4149)-Net in Base 5 — Upper bound on s
There is no (11, 17, 4150)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 763347 364601 > 517 [i]