Best Known (61−35, 61, s)-Nets in Base 81
(61−35, 61, 370)-Net over F81 — Constructive and digital
Digital (26, 61, 370)-net over F81, using
- t-expansion [i] based on digital (16, 61, 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
(61−35, 61, 500)-Net over F81 — Digital
Digital (26, 61, 500)-net over F81, using
- net from sequence [i] based on digital (26, 499)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 26 and N(F) ≥ 500, using
(61−35, 61, 488289)-Net in Base 81 — Upper bound on s
There is no (26, 61, 488290)-net in base 81, because
- 1 times m-reduction [i] would yield (26, 60, 488290)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 3 229301 165970 070404 186081 361338 752181 516430 392928 702464 486248 115415 818095 528703 892444 789723 971155 964251 232168 202401 > 8160 [i]