Best Known (78, 78+28, s)-Nets in Base 7
(78, 78+28, 688)-Net over F7 — Constructive and digital
Digital (78, 106, 688)-net over F7, using
- t-expansion [i] based on digital (76, 106, 688)-net over F7, using
- 4 times m-reduction [i] based on digital (76, 110, 688)-net over F7, using
- trace code for nets [i] based on digital (21, 55, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- trace code for nets [i] based on digital (21, 55, 344)-net over F49, using
- 4 times m-reduction [i] based on digital (76, 110, 688)-net over F7, using
(78, 78+28, 3798)-Net over F7 — Digital
Digital (78, 106, 3798)-net over F7, using
(78, 78+28, 2522925)-Net in Base 7 — Upper bound on s
There is no (78, 106, 2522926)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 380534 130141 451400 029463 175406 885026 515062 821599 651475 207236 549904 185851 809663 297165 984709 > 7106 [i]