Best Known (179, 179+49, s)-Nets in Base 4
(179, 179+49, 1060)-Net over F4 — Constructive and digital
Digital (179, 228, 1060)-net over F4, using
- trace code for nets [i] based on digital (8, 57, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
(179, 179+49, 4551)-Net over F4 — Digital
Digital (179, 228, 4551)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4228, 4551, F4, 49) (dual of [4551, 4323, 50]-code), using
- 443 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 4 times 0, 1, 9 times 0, 1, 19 times 0, 1, 34 times 0, 1, 58 times 0, 1, 83 times 0, 1, 105 times 0, 1, 120 times 0) [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]
- 443 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 4 times 0, 1, 9 times 0, 1, 19 times 0, 1, 34 times 0, 1, 58 times 0, 1, 83 times 0, 1, 105 times 0, 1, 120 times 0) [i] based on linear OA(4217, 4097, F4, 49) (dual of [4097, 3880, 50]-code), using
(179, 179+49, 1617038)-Net in Base 4 — Upper bound on s
There is no (179, 228, 1617039)-net in base 4, because
- 1 times m-reduction [i] would yield (179, 227, 1617039)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 46518 103466 103965 397821 786755 987708 964280 794429 399312 527888 570236 476277 470093 052190 359534 401764 595067 864368 583948 482110 320776 786378 902264 > 4227 [i]