Best Known (188, 188+56, s)-Nets in Base 4
(188, 188+56, 1048)-Net over F4 — Constructive and digital
Digital (188, 244, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 61, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
(188, 188+56, 3362)-Net over F4 — Digital
Digital (188, 244, 3362)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4244, 3362, F4, 56) (dual of [3362, 3118, 57]-code), using
- 3117 step Varšamov–Edel lengthening with (ri) = (15, 7, 4, 3, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 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, 7 times 0, 1, 7 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, 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, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 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, 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, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 23 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 37 times 0, 1, 38 times 0, 1, 39 times 0, 1, 40 times 0, 1, 41 times 0, 1, 42 times 0, 1, 43 times 0, 1, 45 times 0, 1, 45 times 0, 1, 47 times 0, 1, 48 times 0, 1, 50 times 0, 1, 51 times 0, 1, 52 times 0, 1, 53 times 0, 1, 55 times 0, 1, 56 times 0, 1, 58 times 0, 1, 59 times 0, 1, 61 times 0, 1, 63 times 0, 1, 64 times 0, 1, 66 times 0, 1, 67 times 0, 1, 70 times 0, 1, 71 times 0, 1, 73 times 0, 1, 75 times 0, 1, 77 times 0, 1, 79 times 0, 1, 81 times 0) [i] based on linear OA(456, 57, F4, 56) (dual of [57, 1, 57]-code or 57-arc in PG(55,4)), using
- dual of repetition code with length 57 [i]
- 3117 step Varšamov–Edel lengthening with (ri) = (15, 7, 4, 3, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 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, 7 times 0, 1, 7 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, 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, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 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, 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, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 23 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 37 times 0, 1, 38 times 0, 1, 39 times 0, 1, 40 times 0, 1, 41 times 0, 1, 42 times 0, 1, 43 times 0, 1, 45 times 0, 1, 45 times 0, 1, 47 times 0, 1, 48 times 0, 1, 50 times 0, 1, 51 times 0, 1, 52 times 0, 1, 53 times 0, 1, 55 times 0, 1, 56 times 0, 1, 58 times 0, 1, 59 times 0, 1, 61 times 0, 1, 63 times 0, 1, 64 times 0, 1, 66 times 0, 1, 67 times 0, 1, 70 times 0, 1, 71 times 0, 1, 73 times 0, 1, 75 times 0, 1, 77 times 0, 1, 79 times 0, 1, 81 times 0) [i] based on linear OA(456, 57, F4, 56) (dual of [57, 1, 57]-code or 57-arc in PG(55,4)), using
(188, 188+56, 664341)-Net in Base 4 — Upper bound on s
There is no (188, 244, 664342)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 799 171728 289859 626886 573044 387338 264809 092184 292195 011009 558290 355915 865813 566894 026312 070423 267426 238089 797591 809639 377984 018288 759892 578376 230944 > 4244 [i]