Best Known (59, 59+26, s)-Nets in Base 7
(59, 59+26, 206)-Net over F7 — Constructive and digital
Digital (59, 85, 206)-net over F7, using
- 1 times m-reduction [i] based on digital (59, 86, 206)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (15, 28, 102)-net over F7, using
- trace code for nets [i] based on digital (1, 14, 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, 14, 51)-net over F49, using
- digital (31, 58, 104)-net over F7, using
- trace code for nets [i] based on digital (2, 29, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49, using
- trace code for nets [i] based on digital (2, 29, 52)-net over F49, using
- digital (15, 28, 102)-net over F7, using
- (u, u+v)-construction [i] based on
(59, 59+26, 1280)-Net over F7 — Digital
Digital (59, 85, 1280)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(785, 1280, F7, 26) (dual of [1280, 1195, 27]-code), using
- 1194 step Varšamov–Edel lengthening with (ri) = (5, 2, 2, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 28 times 0, 1, 30 times 0, 1, 32 times 0, 1, 35 times 0, 1, 39 times 0, 1, 41 times 0, 1, 45 times 0, 1, 49 times 0, 1, 53 times 0, 1, 58 times 0, 1, 62 times 0, 1, 68 times 0, 1, 73 times 0, 1, 79 times 0, 1, 86 times 0, 1, 93 times 0) [i] based on linear OA(726, 27, F7, 26) (dual of [27, 1, 27]-code or 27-arc in PG(25,7)), using
- dual of repetition code with length 27 [i]
- 1194 step Varšamov–Edel lengthening with (ri) = (5, 2, 2, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 28 times 0, 1, 30 times 0, 1, 32 times 0, 1, 35 times 0, 1, 39 times 0, 1, 41 times 0, 1, 45 times 0, 1, 49 times 0, 1, 53 times 0, 1, 58 times 0, 1, 62 times 0, 1, 68 times 0, 1, 73 times 0, 1, 79 times 0, 1, 86 times 0, 1, 93 times 0) [i] based on linear OA(726, 27, F7, 26) (dual of [27, 1, 27]-code or 27-arc in PG(25,7)), using
(59, 59+26, 316872)-Net in Base 7 — Upper bound on s
There is no (59, 85, 316873)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 681301 752205 469362 827537 252209 142357 062334 604171 585625 116359 254281 978903 > 785 [i]