Best Known (174−39, 174, s)-Nets in Base 4
(174−39, 174, 1044)-Net over F4 — Constructive and digital
Digital (135, 174, 1044)-net over F4, using
- 42 times duplication [i] based on digital (133, 172, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 43, 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, 43, 261)-net over F256, using
(174−39, 174, 2880)-Net over F4 — Digital
Digital (135, 174, 2880)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4174, 2880, F4, 39) (dual of [2880, 2706, 40]-code), using
- 2705 step Varšamov–Edel lengthening with (ri) = (11, 5, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 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, 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, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 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, 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, 15 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, 19 times 0, 1, 20 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, 27 times 0, 1, 28 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 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, 56 times 0, 1, 57 times 0, 1, 59 times 0, 1, 62 times 0, 1, 64 times 0, 1, 67 times 0, 1, 69 times 0, 1, 72 times 0, 1, 75 times 0, 1, 77 times 0, 1, 80 times 0, 1, 84 times 0, 1, 86 times 0, 1, 90 times 0, 1, 93 times 0, 1, 97 times 0, 1, 101 times 0) [i] based on linear OA(439, 40, F4, 39) (dual of [40, 1, 40]-code or 40-arc in PG(38,4)), using
- dual of repetition code with length 40 [i]
- 2705 step Varšamov–Edel lengthening with (ri) = (11, 5, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 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, 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, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 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, 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, 15 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, 19 times 0, 1, 20 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, 27 times 0, 1, 28 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 32 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, 56 times 0, 1, 57 times 0, 1, 59 times 0, 1, 62 times 0, 1, 64 times 0, 1, 67 times 0, 1, 69 times 0, 1, 72 times 0, 1, 75 times 0, 1, 77 times 0, 1, 80 times 0, 1, 84 times 0, 1, 86 times 0, 1, 90 times 0, 1, 93 times 0, 1, 97 times 0, 1, 101 times 0) [i] based on linear OA(439, 40, F4, 39) (dual of [40, 1, 40]-code or 40-arc in PG(38,4)), using
(174−39, 174, 801679)-Net in Base 4 — Upper bound on s
There is no (135, 174, 801680)-net in base 4, because
- 1 times m-reduction [i] would yield (135, 173, 801680)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 143 346460 307661 858180 891782 599573 535899 431929 975673 975360 534423 964112 269502 785803 942765 130629 718662 628984 > 4173 [i]