Best Known (41, 41+18, s)-Nets in Base 7
(41, 41+18, 204)-Net over F7 — Constructive and digital
Digital (41, 59, 204)-net over F7, using
- 1 times m-reduction [i] based on digital (41, 60, 204)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (11, 20, 102)-net over F7, using
- trace code for nets [i] based on digital (1, 10, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- trace code for nets [i] based on digital (1, 10, 51)-net over F49, using
- digital (21, 40, 102)-net over F7, using
- trace code for nets [i] based on digital (1, 20, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49 (see above)
- trace code for nets [i] based on digital (1, 20, 51)-net over F49, using
- digital (11, 20, 102)-net over F7, using
- (u, u+v)-construction [i] based on
(41, 41+18, 1034)-Net over F7 — Digital
Digital (41, 59, 1034)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(759, 1034, F7, 18) (dual of [1034, 975, 19]-code), using
- 974 step Varšamov–Edel lengthening with (ri) = (3, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 11 times 0, 1, 12 times 0, 1, 14 times 0, 1, 16 times 0, 1, 18 times 0, 1, 20 times 0, 1, 23 times 0, 1, 26 times 0, 1, 30 times 0, 1, 33 times 0, 1, 37 times 0, 1, 43 times 0, 1, 48 times 0, 1, 53 times 0, 1, 61 times 0, 1, 68 times 0, 1, 77 times 0, 1, 86 times 0, 1, 97 times 0, 1, 109 times 0) [i] based on linear OA(718, 19, F7, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,7)), using
- dual of repetition code with length 19 [i]
- 974 step Varšamov–Edel lengthening with (ri) = (3, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 11 times 0, 1, 12 times 0, 1, 14 times 0, 1, 16 times 0, 1, 18 times 0, 1, 20 times 0, 1, 23 times 0, 1, 26 times 0, 1, 30 times 0, 1, 33 times 0, 1, 37 times 0, 1, 43 times 0, 1, 48 times 0, 1, 53 times 0, 1, 61 times 0, 1, 68 times 0, 1, 77 times 0, 1, 86 times 0, 1, 97 times 0, 1, 109 times 0) [i] based on linear OA(718, 19, F7, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,7)), using
(41, 41+18, 239705)-Net in Base 7 — Upper bound on s
There is no (41, 59, 239706)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 72 576838 414045 247424 784133 314644 367512 298448 282893 > 759 [i]