Best Known (171−40, 171, s)-Nets in Base 4
(171−40, 171, 1036)-Net over F4 — Constructive and digital
Digital (131, 171, 1036)-net over F4, using
- 1 times m-reduction [i] based on digital (131, 172, 1036)-net over F4, using
- trace code for nets [i] based on digital (2, 43, 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, 43, 259)-net over F256, using
(171−40, 171, 2259)-Net over F4 — Digital
Digital (131, 171, 2259)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4171, 2259, F4, 40) (dual of [2259, 2088, 41]-code), using
- 2087 step Varšamov–Edel lengthening with (ri) = (11, 5, 3, 2, 2, 1, 2, 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, 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, 0, 0, 0, 1, 4 times 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, 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, 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, 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, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 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, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 47 times 0, 1, 49 times 0, 1, 51 times 0, 1, 53 times 0, 1, 55 times 0, 1, 57 times 0, 1, 59 times 0, 1, 61 times 0, 1, 63 times 0, 1, 66 times 0, 1, 68 times 0, 1, 71 times 0, 1, 73 times 0, 1, 77 times 0) [i] based on linear OA(440, 41, F4, 40) (dual of [41, 1, 41]-code or 41-arc in PG(39,4)), using
- dual of repetition code with length 41 [i]
- 2087 step Varšamov–Edel lengthening with (ri) = (11, 5, 3, 2, 2, 1, 2, 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, 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, 0, 0, 0, 1, 4 times 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, 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, 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, 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, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 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, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 46 times 0, 1, 47 times 0, 1, 49 times 0, 1, 51 times 0, 1, 53 times 0, 1, 55 times 0, 1, 57 times 0, 1, 59 times 0, 1, 61 times 0, 1, 63 times 0, 1, 66 times 0, 1, 68 times 0, 1, 71 times 0, 1, 73 times 0, 1, 77 times 0) [i] based on linear OA(440, 41, F4, 40) (dual of [41, 1, 41]-code or 41-arc in PG(39,4)), using
(171−40, 171, 388847)-Net in Base 4 — Upper bound on s
There is no (131, 171, 388848)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 8 958988 476183 004392 199895 105641 004017 237072 767137 745297 308620 228806 225517 535522 061668 994875 887507 868446 > 4171 [i]