Best Known (37−11, 37, s)-Nets in Base 8
(37−11, 37, 819)-Net over F8 — Constructive and digital
Digital (26, 37, 819)-net over F8, using
- net defined by OOA [i] based on linear OOA(837, 819, F8, 11, 11) (dual of [(819, 11), 8972, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(837, 4096, F8, 11) (dual of [4096, 4059, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, 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(837, 4096, F8, 11) (dual of [4096, 4059, 12]-code), using
(37−11, 37, 2422)-Net over F8 — Digital
Digital (26, 37, 2422)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(837, 2422, F8, 11) (dual of [2422, 2385, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(837, 4096, F8, 11) (dual of [4096, 4059, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(837, 4096, F8, 11) (dual of [4096, 4059, 12]-code), using
(37−11, 37, 1183001)-Net in Base 8 — Upper bound on s
There is no (26, 37, 1183002)-net in base 8, because
- 1 times m-reduction [i] would yield (26, 36, 1183002)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 324 519897 785826 261674 654053 317078 > 836 [i]