Best Known (21, 21+45, s)-Nets in Base 81
(21, 21+45, 370)-Net over F81 — Constructive and digital
Digital (21, 66, 370)-net over F81, using
- t-expansion [i] based on digital (16, 66, 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
(21, 21+45, 49246)-Net in Base 81 — Upper bound on s
There is no (21, 66, 49247)-net in base 81, because
- 1 times m-reduction [i] would yield (21, 65, 49247)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 11263 112565 347380 266759 609007 549941 573998 563433 864851 154431 820114 766519 589369 269920 317330 338439 010609 183452 391679 688434 629921 > 8165 [i]