Best Known (82−49, 82, s)-Nets in Base 7
(82−49, 82, 35)-Net over F7 — Constructive and digital
Digital (33, 82, 35)-net over F7, using
- net from sequence [i] based on digital (33, 34)-sequence over F7, using
(82−49, 82, 96)-Net over F7 — Digital
Digital (33, 82, 96)-net over F7, using
- net from sequence [i] based on digital (33, 95)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 33 and N(F) ≥ 96, using
(82−49, 82, 1147)-Net in Base 7 — Upper bound on s
There is no (33, 82, 1148)-net in base 7, because
- 1 times m-reduction [i] would yield (33, 81, 1148)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 288 883907 458511 836461 403921 517539 248724 656009 840111 245431 866190 715329 > 781 [i]