Best Known (172, 172+48, s)-Nets in Base 4
(172, 172+48, 1056)-Net over F4 — Constructive and digital
Digital (172, 220, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 55, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
(172, 172+48, 4150)-Net over F4 — Digital
Digital (172, 220, 4150)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4220, 4150, F4, 48) (dual of [4150, 3930, 49]-code), using
- 50 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 12 times 0, 1, 33 times 0) [i] based on linear OA(4216, 4096, F4, 48) (dual of [4096, 3880, 49]-code), using
- 1 times truncation [i] based on linear OA(4217, 4097, F4, 49) (dual of [4097, 3880, 50]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4217, 4097, F4, 49) (dual of [4097, 3880, 50]-code), using
- 50 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 12 times 0, 1, 33 times 0) [i] based on linear OA(4216, 4096, F4, 48) (dual of [4096, 3880, 49]-code), using
(172, 172+48, 1079237)-Net in Base 4 — Upper bound on s
There is no (172, 220, 1079238)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 839267 100375 187958 692582 812205 705377 788121 942237 466475 729965 593876 544705 498853 459518 771489 480765 234030 757110 605956 376894 584019 954056 > 4220 [i]