Best Known (104−31, 104, s)-Nets in Base 7
(104−31, 104, 688)-Net over F7 — Constructive and digital
Digital (73, 104, 688)-net over F7, using
- trace code for nets [i] based on digital (21, 52, 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
(104−31, 104, 1722)-Net over F7 — Digital
Digital (73, 104, 1722)-net over F7, using
(104−31, 104, 680167)-Net in Base 7 — Upper bound on s
There is no (73, 104, 680168)-net in base 7, because
- 1 times m-reduction [i] would yield (73, 103, 680168)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 1109 438077 504059 842629 703875 162319 333629 995516 177716 851815 533195 406093 860490 905491 440193 > 7103 [i]