Best Known (187−46, 187, s)-Nets in Base 4
(187−46, 187, 1028)-Net over F4 — Constructive and digital
Digital (141, 187, 1028)-net over F4, using
- 1 times m-reduction [i] based on digital (141, 188, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 47, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 47, 257)-net over F256, using
(187−46, 187, 1889)-Net over F4 — Digital
Digital (141, 187, 1889)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4187, 1889, F4, 46) (dual of [1889, 1702, 47]-code), using
- 1701 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) [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]
- 1701 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) [i] based on linear OA(446, 47, F4, 46) (dual of [47, 1, 47]-code or 47-arc in PG(45,4)), using
(187−46, 187, 246780)-Net in Base 4 — Upper bound on s
There is no (141, 187, 246781)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 38478 620197 259668 928584 424886 902790 428468 992745 443649 464009 828185 772000 451336 098177 459979 521263 298236 981096 984856 > 4187 [i]