Best Known (221−48, 221, s)-Nets in Base 4
(221−48, 221, 1056)-Net over F4 — Constructive and digital
Digital (173, 221, 1056)-net over F4, using
- 41 times duplication [i] based on 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
- trace code for nets [i] based on digital (7, 55, 264)-net over F256, using
(221−48, 221, 4217)-Net over F4 — Digital
Digital (173, 221, 4217)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4221, 4217, F4, 48) (dual of [4217, 3996, 49]-code), using
- 116 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 12 times 0, 1, 33 times 0, 1, 65 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
- 116 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 12 times 0, 1, 33 times 0, 1, 65 times 0) [i] based on linear OA(4216, 4096, F4, 48) (dual of [4096, 3880, 49]-code), using
(221−48, 221, 1143413)-Net in Base 4 — Upper bound on s
There is no (173, 221, 1143414)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 11 357070 655420 982678 704989 391352 924180 522674 179002 822832 005752 568155 237230 805953 071561 707023 074993 045043 624067 880258 804821 269762 008764 > 4221 [i]