Best Known (17, 24, s)-Nets in Base 7
(17, 24, 799)-Net over F7 — Constructive and digital
Digital (17, 24, 799)-net over F7, using
- net defined by OOA [i] based on linear OOA(724, 799, F7, 7, 7) (dual of [(799, 7), 5569, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(724, 2398, F7, 7) (dual of [2398, 2374, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(724, 2400, F7, 7) (dual of [2400, 2376, 8]-code), using
- 1 times truncation [i] based on linear OA(725, 2401, F7, 8) (dual of [2401, 2376, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 1 times truncation [i] based on linear OA(725, 2401, F7, 8) (dual of [2401, 2376, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(724, 2400, F7, 7) (dual of [2400, 2376, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(724, 2398, F7, 7) (dual of [2398, 2374, 8]-code), using
(17, 24, 2400)-Net over F7 — Digital
Digital (17, 24, 2400)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(724, 2400, F7, 7) (dual of [2400, 2376, 8]-code), using
- 1 times truncation [i] based on linear OA(725, 2401, F7, 8) (dual of [2401, 2376, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 1 times truncation [i] based on linear OA(725, 2401, F7, 8) (dual of [2401, 2376, 9]-code), using
(17, 24, 912676)-Net in Base 7 — Upper bound on s
There is no (17, 24, 912677)-net in base 7, because
- 1 times m-reduction [i] would yield (17, 23, 912677)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 27 368812 899826 629175 > 723 [i]