Best Known (113, 113+34, s)-Nets in Base 4
(113, 113+34, 1036)-Net over F4 — Constructive and digital
Digital (113, 147, 1036)-net over F4, using
- 1 times m-reduction [i] based on digital (113, 148, 1036)-net over F4, using
- trace code for nets [i] based on digital (2, 37, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- trace code for nets [i] based on digital (2, 37, 259)-net over F256, using
(113, 113+34, 2126)-Net over F4 — Digital
Digital (113, 147, 2126)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4147, 2126, F4, 34) (dual of [2126, 1979, 35]-code), using
- 1978 step Varšamov–Edel lengthening with (ri) = (9, 5, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 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, 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, 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, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 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, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 39 times 0, 1, 40 times 0, 1, 42 times 0, 1, 45 times 0, 1, 46 times 0, 1, 48 times 0, 1, 50 times 0, 1, 53 times 0, 1, 55 times 0, 1, 58 times 0, 1, 60 times 0, 1, 62 times 0, 1, 66 times 0, 1, 68 times 0, 1, 71 times 0, 1, 75 times 0, 1, 78 times 0, 1, 81 times 0, 1, 85 times 0) [i] based on linear OA(434, 35, F4, 34) (dual of [35, 1, 35]-code or 35-arc in PG(33,4)), using
- dual of repetition code with length 35 [i]
- 1978 step Varšamov–Edel lengthening with (ri) = (9, 5, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 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, 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, 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, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 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, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 39 times 0, 1, 40 times 0, 1, 42 times 0, 1, 45 times 0, 1, 46 times 0, 1, 48 times 0, 1, 50 times 0, 1, 53 times 0, 1, 55 times 0, 1, 58 times 0, 1, 60 times 0, 1, 62 times 0, 1, 66 times 0, 1, 68 times 0, 1, 71 times 0, 1, 75 times 0, 1, 78 times 0, 1, 81 times 0, 1, 85 times 0) [i] based on linear OA(434, 35, F4, 34) (dual of [35, 1, 35]-code or 35-arc in PG(33,4)), using
(113, 113+34, 384464)-Net in Base 4 — Upper bound on s
There is no (113, 147, 384465)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 31828 855077 079755 475593 945480 353472 287862 269207 510884 724474 581108 589082 082009 913780 617300 > 4147 [i]