Best Known (224−48, 224, s)-Nets in Base 4
(224−48, 224, 1060)-Net over F4 — Constructive and digital
Digital (176, 224, 1060)-net over F4, using
- trace code for nets [i] based on digital (8, 56, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
(224−48, 224, 4558)-Net over F4 — Digital
Digital (176, 224, 4558)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4224, 4558, F4, 48) (dual of [4558, 4334, 49]-code), using
- 454 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 12 times 0, 1, 33 times 0, 1, 65 times 0, 1, 95 times 0, 1, 115 times 0, 1, 125 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
- 454 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 12 times 0, 1, 33 times 0, 1, 65 times 0, 1, 95 times 0, 1, 115 times 0, 1, 125 times 0) [i] based on linear OA(4216, 4096, F4, 48) (dual of [4096, 3880, 49]-code), using
(224−48, 224, 1359758)-Net in Base 4 — Upper bound on s
There is no (176, 224, 1359759)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 726 842853 029554 870566 284355 982834 015744 743697 309262 606468 083902 456520 989113 556537 341441 366936 431271 032417 085392 530454 968425 680902 859336 > 4224 [i]