Best Known (104, 121, s)-Nets in Base 2
(104, 121, 4096)-Net over F2 — Constructive and digital
Digital (104, 121, 4096)-net over F2, using
- net defined by OOA [i] based on linear OOA(2121, 4096, F2, 17, 17) (dual of [(4096, 17), 69511, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2121, 32769, F2, 17) (dual of [32769, 32648, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(2121, 32769, F2, 17) (dual of [32769, 32648, 18]-code), using
(104, 121, 6553)-Net over F2 — Digital
Digital (104, 121, 6553)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2121, 6553, F2, 5, 17) (dual of [(6553, 5), 32644, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2121, 32765, F2, 17) (dual of [32765, 32644, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2121, 32767, F2, 17) (dual of [32767, 32646, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(2121, 32767, F2, 17) (dual of [32767, 32646, 18]-code), using
- OOA 5-folding [i] based on linear OA(2121, 32765, F2, 17) (dual of [32765, 32644, 18]-code), using
(104, 121, 123338)-Net in Base 2 — Upper bound on s
There is no (104, 121, 123339)-net in base 2, because
- 1 times m-reduction [i] would yield (104, 120, 123339)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 329250 330835 272639 866217 098944 286037 > 2120 [i]