Best Known (70−43, 70, s)-Nets in Base 7
(70−43, 70, 32)-Net over F7 — Constructive and digital
Digital (27, 70, 32)-net over F7, using
- net from sequence [i] based on digital (27, 31)-sequence over F7, using
(70−43, 70, 78)-Net over F7 — Digital
Digital (27, 70, 78)-net over F7, using
- net from sequence [i] based on digital (27, 77)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 27 and N(F) ≥ 78, using
(70−43, 70, 851)-Net in Base 7 — Upper bound on s
There is no (27, 70, 852)-net in base 7, because
- 1 times m-reduction [i] would yield (27, 69, 852)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 20640 737456 369042 191233 132143 539412 538005 628593 176287 376153 > 769 [i]