Best Known (27, 27+19, s)-Nets in Base 7
(27, 27+19, 108)-Net over F7 — Constructive and digital
Digital (27, 46, 108)-net over F7, using
- trace code for nets [i] based on digital (4, 23, 54)-net over F49, using
- net from sequence [i] based on digital (4, 53)-sequence over F49, using
(27, 27+19, 195)-Net over F7 — Digital
Digital (27, 46, 195)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(746, 195, F7, 19) (dual of [195, 149, 20]-code), using
- 9 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 6 times 0) [i] based on linear OA(744, 184, F7, 19) (dual of [184, 140, 20]-code), using
- trace code [i] based on linear OA(4922, 92, F49, 19) (dual of [92, 70, 20]-code), using
- extended algebraic-geometric code AGe(F,72P) [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- trace code [i] based on linear OA(4922, 92, F49, 19) (dual of [92, 70, 20]-code), using
- 9 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 6 times 0) [i] based on linear OA(744, 184, F7, 19) (dual of [184, 140, 20]-code), using
(27, 27+19, 11611)-Net in Base 7 — Upper bound on s
There is no (27, 46, 11612)-net in base 7, because
- 1 times m-reduction [i] would yield (27, 45, 11612)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 107 056256 168306 597548 833852 848465 133097 > 745 [i]