Best Known (179, 179+48, s)-Nets in Base 4
(179, 179+48, 1060)-Net over F4 — Constructive and digital
Digital (179, 227, 1060)-net over F4, using
- 1 times m-reduction [i] based on 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
- trace code for nets [i] based on digital (8, 57, 265)-net over F256, using
(179, 179+48, 4976)-Net over F4 — Digital
Digital (179, 227, 4976)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4227, 4976, F4, 48) (dual of [4976, 4749, 49]-code), using
- 4748 step Varšamov–Edel lengthening with (ri) = (13, 6, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 37 times 0, 1, 38 times 0, 1, 40 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 45 times 0, 1, 46 times 0, 1, 48 times 0, 1, 49 times 0, 1, 51 times 0, 1, 52 times 0, 1, 54 times 0, 1, 56 times 0, 1, 57 times 0, 1, 60 times 0, 1, 61 times 0, 1, 63 times 0, 1, 65 times 0, 1, 66 times 0, 1, 69 times 0, 1, 71 times 0, 1, 73 times 0, 1, 76 times 0, 1, 78 times 0, 1, 80 times 0, 1, 83 times 0, 1, 85 times 0, 1, 88 times 0, 1, 90 times 0, 1, 93 times 0, 1, 96 times 0, 1, 99 times 0, 1, 102 times 0, 1, 105 times 0, 1, 109 times 0, 1, 112 times 0, 1, 115 times 0, 1, 118 times 0, 1, 122 times 0, 1, 126 times 0, 1, 130 times 0, 1, 134 times 0, 1, 138 times 0, 1, 142 times 0) [i] based on linear OA(448, 49, F4, 48) (dual of [49, 1, 49]-code or 49-arc in PG(47,4)), using
- dual of repetition code with length 49 [i]
- 4748 step Varšamov–Edel lengthening with (ri) = (13, 6, 4, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 37 times 0, 1, 38 times 0, 1, 40 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 45 times 0, 1, 46 times 0, 1, 48 times 0, 1, 49 times 0, 1, 51 times 0, 1, 52 times 0, 1, 54 times 0, 1, 56 times 0, 1, 57 times 0, 1, 60 times 0, 1, 61 times 0, 1, 63 times 0, 1, 65 times 0, 1, 66 times 0, 1, 69 times 0, 1, 71 times 0, 1, 73 times 0, 1, 76 times 0, 1, 78 times 0, 1, 80 times 0, 1, 83 times 0, 1, 85 times 0, 1, 88 times 0, 1, 90 times 0, 1, 93 times 0, 1, 96 times 0, 1, 99 times 0, 1, 102 times 0, 1, 105 times 0, 1, 109 times 0, 1, 112 times 0, 1, 115 times 0, 1, 118 times 0, 1, 122 times 0, 1, 126 times 0, 1, 130 times 0, 1, 134 times 0, 1, 138 times 0, 1, 142 times 0) [i] based on linear OA(448, 49, F4, 48) (dual of [49, 1, 49]-code or 49-arc in PG(47,4)), using
(179, 179+48, 1617038)-Net in Base 4 — Upper bound on s
There is no (179, 227, 1617039)-net in base 4, because
- 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]