Best Known (145−25, 145, s)-Nets in Base 2
(145−25, 145, 341)-Net over F2 — Constructive and digital
Digital (120, 145, 341)-net over F2, using
- net defined by OOA [i] based on linear OOA(2145, 341, F2, 25, 25) (dual of [(341, 25), 8380, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2145, 4093, F2, 25) (dual of [4093, 3948, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2145, 4096, F2, 25) (dual of [4096, 3951, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(2145, 4096, F2, 25) (dual of [4096, 3951, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2145, 4093, F2, 25) (dual of [4093, 3948, 26]-code), using
(145−25, 145, 1024)-Net over F2 — Digital
Digital (120, 145, 1024)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2145, 1024, F2, 4, 25) (dual of [(1024, 4), 3951, 26]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2145, 4096, F2, 25) (dual of [4096, 3951, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- OOA 4-folding [i] based on linear OA(2145, 4096, F2, 25) (dual of [4096, 3951, 26]-code), using
(145−25, 145, 21645)-Net in Base 2 — Upper bound on s
There is no (120, 145, 21646)-net in base 2, because
- 1 times m-reduction [i] would yield (120, 144, 21646)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 22 305141 686434 419845 648876 645000 800586 267789 > 2144 [i]