Best Known (69−49, 69, s)-Nets in Base 81
(69−49, 69, 370)-Net over F81 — Constructive and digital
Digital (20, 69, 370)-net over F81, using
- t-expansion [i] based on digital (16, 69, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(69−49, 69, 31295)-Net in Base 81 — Upper bound on s
There is no (20, 69, 31296)-net in base 81, because
- 1 times m-reduction [i] would yield (20, 68, 31296)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 5985 699980 326922 891102 752914 545524 895564 941188 395940 066005 201948 335576 799525 505874 155184 068569 074408 759921 120919 889953 136959 774721 > 8168 [i]