Best Known (72, 72+26, s)-Nets in Base 7
(72, 72+26, 688)-Net over F7 — Constructive and digital
Digital (72, 98, 688)-net over F7, using
- 4 times m-reduction [i] based on digital (72, 102, 688)-net over F7, using
- trace code for nets [i] based on digital (21, 51, 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, 51, 344)-net over F49, using
(72, 72+26, 3498)-Net over F7 — Digital
Digital (72, 98, 3498)-net over F7, using
(72, 72+26, 2218157)-Net in Base 7 — Upper bound on s
There is no (72, 98, 2218158)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 66009 879013 314454 303045 401903 244191 870908 104390 776119 809602 420253 980241 830458 851069 > 798 [i]