Best Known (219−46, 219, s)-Nets in Base 4
(219−46, 219, 1060)-Net over F4 — Constructive and digital
Digital (173, 219, 1060)-net over F4, using
- 1 times m-reduction [i] based on digital (173, 220, 1060)-net over F4, using
- trace code for nets [i] based on digital (8, 55, 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, 55, 265)-net over F256, using
(219−46, 219, 5024)-Net over F4 — Digital
Digital (173, 219, 5024)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4219, 5024, F4, 46) (dual of [5024, 4805, 47]-code), using
- 4804 step Varšamov–Edel lengthening with (ri) = (13, 5, 4, 2, 2, 2, 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, 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, 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, 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, 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, 10 times 0, 1, 9 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, 13 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 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, 23 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 28 times 0, 1, 30 times 0, 1, 30 times 0, 1, 32 times 0, 1, 32 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, 50 times 0, 1, 51 times 0, 1, 53 times 0, 1, 55 times 0, 1, 56 times 0, 1, 58 times 0, 1, 60 times 0, 1, 62 times 0, 1, 64 times 0, 1, 66 times 0, 1, 69 times 0, 1, 70 times 0, 1, 73 times 0, 1, 75 times 0, 1, 77 times 0, 1, 80 times 0, 1, 83 times 0, 1, 85 times 0, 1, 88 times 0, 1, 90 times 0, 1, 94 times 0, 1, 97 times 0, 1, 99 times 0, 1, 103 times 0, 1, 106 times 0, 1, 110 times 0, 1, 113 times 0, 1, 116 times 0, 1, 120 times 0, 1, 124 times 0, 1, 128 times 0, 1, 133 times 0, 1, 136 times 0, 1, 141 times 0, 1, 145 times 0, 1, 150 times 0) [i] based on linear OA(446, 47, F4, 46) (dual of [47, 1, 47]-code or 47-arc in PG(45,4)), using
- dual of repetition code with length 47 [i]
- 4804 step Varšamov–Edel lengthening with (ri) = (13, 5, 4, 2, 2, 2, 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, 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, 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, 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, 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, 10 times 0, 1, 9 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, 13 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 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, 23 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 28 times 0, 1, 30 times 0, 1, 30 times 0, 1, 32 times 0, 1, 32 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, 50 times 0, 1, 51 times 0, 1, 53 times 0, 1, 55 times 0, 1, 56 times 0, 1, 58 times 0, 1, 60 times 0, 1, 62 times 0, 1, 64 times 0, 1, 66 times 0, 1, 69 times 0, 1, 70 times 0, 1, 73 times 0, 1, 75 times 0, 1, 77 times 0, 1, 80 times 0, 1, 83 times 0, 1, 85 times 0, 1, 88 times 0, 1, 90 times 0, 1, 94 times 0, 1, 97 times 0, 1, 99 times 0, 1, 103 times 0, 1, 106 times 0, 1, 110 times 0, 1, 113 times 0, 1, 116 times 0, 1, 120 times 0, 1, 124 times 0, 1, 128 times 0, 1, 133 times 0, 1, 136 times 0, 1, 141 times 0, 1, 145 times 0, 1, 150 times 0) [i] based on linear OA(446, 47, F4, 46) (dual of [47, 1, 47]-code or 47-arc in PG(45,4)), using
(219−46, 219, 1698198)-Net in Base 4 — Upper bound on s
There is no (173, 219, 1698199)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 709809 135459 436132 409667 577192 537753 496997 530060 397361 050759 448014 339981 799829 981034 584868 000674 471003 350357 961725 591040 218630 609852 > 4219 [i]