Best Known (197−49, 197, s)-Nets in Base 4
(197−49, 197, 1028)-Net over F4 — Constructive and digital
Digital (148, 197, 1028)-net over F4, using
- 41 times duplication [i] based on digital (147, 196, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 49, 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, 49, 257)-net over F256, using
(197−49, 197, 1872)-Net over F4 — Digital
Digital (148, 197, 1872)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4197, 1872, F4, 49) (dual of [1872, 1675, 50]-code), using
- 1674 step Varšamov–Edel lengthening with (ri) = (14, 6, 3, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 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, 0, 1, 0, 0, 1, 0, 0, 1, 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, 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, 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, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 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, 13 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, 16 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 26 times 0, 1, 28 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0, 1, 37 times 0, 1, 39 times 0, 1, 39 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, 49 times 0, 1, 51 times 0) [i] based on linear OA(449, 50, F4, 49) (dual of [50, 1, 50]-code or 50-arc in PG(48,4)), using
- dual of repetition code with length 50 [i]
- 1674 step Varšamov–Edel lengthening with (ri) = (14, 6, 3, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 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, 0, 1, 0, 0, 1, 0, 0, 1, 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, 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, 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, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 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, 13 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, 16 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 23 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 26 times 0, 1, 28 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 37 times 0, 1, 37 times 0, 1, 39 times 0, 1, 39 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, 49 times 0, 1, 51 times 0) [i] based on linear OA(449, 50, F4, 49) (dual of [50, 1, 50]-code or 50-arc in PG(48,4)), using
(197−49, 197, 269794)-Net in Base 4 — Upper bound on s
There is no (148, 197, 269795)-net in base 4, because
- 1 times m-reduction [i] would yield (148, 196, 269795)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 10087 214764 796057 427204 826365 822088 442304 856371 057556 307924 785544 357530 228814 686092 457676 235541 468081 439536 063319 800324 > 4196 [i]