Best Known (82−43, 82, s)-Nets in Base 81
(82−43, 82, 730)-Net over F81 — Constructive and digital
Digital (39, 82, 730)-net over F81, using
- t-expansion [i] based on digital (36, 82, 730)-net over F81, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
(82−43, 82, 1120)-Net over F81 — Digital
Digital (39, 82, 1120)-net over F81, using
(82−43, 82, 2492872)-Net in Base 81 — Upper bound on s
There is no (39, 82, 2492873)-net in base 81, because
- 1 times m-reduction [i] would yield (39, 81, 2492873)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 38662 202482 525842 105579 389725 816624 756868 549959 140811 506354 115640 479584 332038 399994 651682 590974 427551 386643 119670 301464 150316 555385 195752 040925 540413 370641 > 8181 [i]