Best Known (161, 205, s)-Nets in Base 4
(161, 205, 1056)-Net over F4 — Constructive and digital
Digital (161, 205, 1056)-net over F4, using
- 41 times duplication [i] based on digital (160, 204, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 51, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
- trace code for nets [i] based on digital (7, 51, 264)-net over F256, using
(161, 205, 4261)-Net over F4 — Digital
Digital (161, 205, 4261)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4205, 4261, F4, 44) (dual of [4261, 4056, 45]-code), using
- 159 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 12 times 0, 1, 23 times 0, 1, 43 times 0, 1, 69 times 0) [i] based on linear OA(4198, 4095, F4, 44) (dual of [4095, 3897, 45]-code), using
- 1 times truncation [i] based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
- an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- 1 times truncation [i] based on linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using
- 159 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 12 times 0, 1, 23 times 0, 1, 43 times 0, 1, 69 times 0) [i] based on linear OA(4198, 4095, F4, 44) (dual of [4095, 3897, 45]-code), using
(161, 205, 1229787)-Net in Base 4 — Upper bound on s
There is no (161, 205, 1229788)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2644 265641 790852 779679 293566 327006 702871 990531 692427 164269 089677 742638 248380 325826 486372 253696 775121 894738 435480 665271 616018 > 4205 [i]