Best Known (82−71, 82, s)-Nets in Base 27
(82−71, 82, 96)-Net over F27 — Constructive and digital
Digital (11, 82, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
(82−71, 82, 100)-Net over F27 — Digital
Digital (11, 82, 100)-net over F27, using
- net from sequence [i] based on digital (11, 99)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 100, using
(82−71, 82, 1080)-Net in Base 27 — Upper bound on s
There is no (11, 82, 1081)-net in base 27, because
- 1 times m-reduction [i] would yield (11, 81, 1081)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 88 838953 074351 778982 423684 469624 243215 483323 603412 577245 773608 193712 356674 689636 816455 937790 362086 823106 525801 369795 > 2781 [i]