Best Known (135, 135+41, s)-Nets in Base 4
(135, 135+41, 1040)-Net over F4 — Constructive and digital
Digital (135, 176, 1040)-net over F4, using
- trace code for nets [i] based on digital (3, 44, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
(135, 135+41, 2363)-Net over F4 — Digital
Digital (135, 176, 2363)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4176, 2363, F4, 41) (dual of [2363, 2187, 42]-code), using
- 2186 step Varšamov–Edel lengthening with (ri) = (11, 5, 3, 3, 2, 1, 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, 1, 0, 0, 1, 0, 0, 1, 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, 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, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 40 times 0, 1, 43 times 0, 1, 44 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 51 times 0, 1, 52 times 0, 1, 54 times 0, 1, 57 times 0, 1, 58 times 0, 1, 61 times 0, 1, 63 times 0, 1, 65 times 0, 1, 67 times 0, 1, 70 times 0, 1, 73 times 0, 1, 75 times 0, 1, 78 times 0) [i] based on linear OA(441, 42, F4, 41) (dual of [42, 1, 42]-code or 42-arc in PG(40,4)), using
- dual of repetition code with length 42 [i]
- 2186 step Varšamov–Edel lengthening with (ri) = (11, 5, 3, 3, 2, 1, 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, 1, 0, 0, 1, 0, 0, 1, 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, 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, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 18 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 29 times 0, 1, 30 times 0, 1, 32 times 0, 1, 33 times 0, 1, 34 times 0, 1, 35 times 0, 1, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 40 times 0, 1, 43 times 0, 1, 44 times 0, 1, 45 times 0, 1, 47 times 0, 1, 49 times 0, 1, 51 times 0, 1, 52 times 0, 1, 54 times 0, 1, 57 times 0, 1, 58 times 0, 1, 61 times 0, 1, 63 times 0, 1, 65 times 0, 1, 67 times 0, 1, 70 times 0, 1, 73 times 0, 1, 75 times 0, 1, 78 times 0) [i] based on linear OA(441, 42, F4, 41) (dual of [42, 1, 42]-code or 42-arc in PG(40,4)), using
(135, 135+41, 513093)-Net in Base 4 — Upper bound on s
There is no (135, 176, 513094)-net in base 4, because
- 1 times m-reduction [i] would yield (135, 175, 513094)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2293 574595 469550 627703 943867 667444 287207 109286 304526 152859 577765 351704 967120 326330 410255 820572 759220 902204 > 4175 [i]