Best Known (26, 37, s)-Nets in Base 7
(26, 37, 480)-Net over F7 — Constructive and digital
Digital (26, 37, 480)-net over F7, using
- net defined by OOA [i] based on linear OOA(737, 480, F7, 11, 11) (dual of [(480, 11), 5243, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(737, 2401, F7, 11) (dual of [2401, 2364, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(737, 2401, F7, 11) (dual of [2401, 2364, 12]-code), using
(26, 37, 1655)-Net over F7 — Digital
Digital (26, 37, 1655)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(737, 1655, F7, 11) (dual of [1655, 1618, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(737, 2401, F7, 11) (dual of [2401, 2364, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(737, 2401, F7, 11) (dual of [2401, 2364, 12]-code), using
(26, 37, 527701)-Net in Base 7 — Upper bound on s
There is no (26, 37, 527702)-net in base 7, because
- 1 times m-reduction [i] would yield (26, 36, 527702)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 2 651736 494836 625698 576051 886077 > 736 [i]