Best Known (190−43, 190, s)-Nets in Base 4
(190−43, 190, 1044)-Net over F4 — Constructive and digital
Digital (147, 190, 1044)-net over F4, using
- 42 times duplication [i] based on digital (145, 188, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 47, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- trace code for nets [i] based on digital (4, 47, 261)-net over F256, using
(190−43, 190, 2934)-Net over F4 — Digital
Digital (147, 190, 2934)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4190, 2934, F4, 43) (dual of [2934, 2744, 44]-code), using
- 2743 step Varšamov–Edel lengthening with (ri) = (12, 5, 3, 3, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 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, 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, 0, 0, 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, 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, 9 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, 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, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 50 times 0, 1, 52 times 0, 1, 54 times 0, 1, 55 times 0, 1, 58 times 0, 1, 59 times 0, 1, 62 times 0, 1, 64 times 0, 1, 66 times 0, 1, 68 times 0, 1, 71 times 0, 1, 73 times 0, 1, 75 times 0, 1, 78 times 0, 1, 81 times 0, 1, 84 times 0, 1, 86 times 0, 1, 90 times 0, 1, 93 times 0) [i] based on linear OA(443, 44, F4, 43) (dual of [44, 1, 44]-code or 44-arc in PG(42,4)), using
- dual of repetition code with length 44 [i]
- 2743 step Varšamov–Edel lengthening with (ri) = (12, 5, 3, 3, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 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, 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, 0, 0, 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, 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, 9 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, 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, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 24 times 0, 1, 24 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 37 times 0, 1, 38 times 0, 1, 39 times 0, 1, 41 times 0, 1, 42 times 0, 1, 44 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 50 times 0, 1, 52 times 0, 1, 54 times 0, 1, 55 times 0, 1, 58 times 0, 1, 59 times 0, 1, 62 times 0, 1, 64 times 0, 1, 66 times 0, 1, 68 times 0, 1, 71 times 0, 1, 73 times 0, 1, 75 times 0, 1, 78 times 0, 1, 81 times 0, 1, 84 times 0, 1, 86 times 0, 1, 90 times 0, 1, 93 times 0) [i] based on linear OA(443, 44, F4, 43) (dual of [44, 1, 44]-code or 44-arc in PG(42,4)), using
(190−43, 190, 758405)-Net in Base 4 — Upper bound on s
There is no (147, 190, 758406)-net in base 4, because
- 1 times m-reduction [i] would yield (147, 189, 758406)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 615664 100216 284727 426686 962274 651779 500523 394636 972187 751090 360644 390243 627916 035725 430128 297027 721330 350778 889736 > 4189 [i]