Best Known (90, 108, s)-Nets in Base 2
(90, 108, 455)-Net over F2 — Constructive and digital
Digital (90, 108, 455)-net over F2, using
- net defined by OOA [i] based on linear OOA(2108, 455, F2, 18, 18) (dual of [(455, 18), 8082, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2108, 4095, F2, 18) (dual of [4095, 3987, 19]-code), using
- 1 times truncation [i] based on linear OA(2109, 4096, F2, 19) (dual of [4096, 3987, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 1 times truncation [i] based on linear OA(2109, 4096, F2, 19) (dual of [4096, 3987, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(2108, 4095, F2, 18) (dual of [4095, 3987, 19]-code), using
(90, 108, 1075)-Net over F2 — Digital
Digital (90, 108, 1075)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2108, 1075, F2, 3, 18) (dual of [(1075, 3), 3117, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2108, 1365, F2, 3, 18) (dual of [(1365, 3), 3987, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2108, 4095, F2, 18) (dual of [4095, 3987, 19]-code), using
- 1 times truncation [i] based on linear OA(2109, 4096, F2, 19) (dual of [4096, 3987, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 1 times truncation [i] based on linear OA(2109, 4096, F2, 19) (dual of [4096, 3987, 20]-code), using
- OOA 3-folding [i] based on linear OA(2108, 4095, F2, 18) (dual of [4095, 3987, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(2108, 1365, F2, 3, 18) (dual of [(1365, 3), 3987, 19]-NRT-code), using
(90, 108, 16973)-Net in Base 2 — Upper bound on s
There is no (90, 108, 16974)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 324 553373 877857 514655 198654 021857 > 2108 [i]