Best Known (90−20, 90, s)-Nets in Base 4
(90−20, 90, 1036)-Net over F4 — Constructive and digital
Digital (70, 90, 1036)-net over F4, using
- 42 times duplication [i] based on digital (68, 88, 1036)-net over F4, using
- trace code for nets [i] based on digital (2, 22, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- trace code for nets [i] based on digital (2, 22, 259)-net over F256, using
(90−20, 90, 2373)-Net over F4 — Digital
Digital (70, 90, 2373)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(490, 2373, F4, 20) (dual of [2373, 2283, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(490, 4095, F4, 20) (dual of [4095, 4005, 21]-code), using
- 1 times truncation [i] based on linear OA(491, 4096, F4, 21) (dual of [4096, 4005, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 1 times truncation [i] based on linear OA(491, 4096, F4, 21) (dual of [4096, 4005, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(490, 4095, F4, 20) (dual of [4095, 4005, 21]-code), using
(90−20, 90, 395718)-Net in Base 4 — Upper bound on s
There is no (70, 90, 395719)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1 532514 214707 250452 543386 279772 577468 099185 128930 134600 > 490 [i]