Best Known (68−61, 68, s)-Nets in Base 81
(68−61, 68, 172)-Net over F81 — Constructive and digital
Digital (7, 68, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
(68−61, 68, 190)-Net over F81 — Digital
Digital (7, 68, 190)-net over F81, using
- t-expansion [i] based on digital (6, 68, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
(68−61, 68, 2739)-Net in Base 81 — Upper bound on s
There is no (7, 68, 2740)-net in base 81, because
- 1 times m-reduction [i] would yield (7, 67, 2740)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 74 477098 147228 222080 559973 083144 889181 366090 985666 889544 900867 253768 436494 910892 059932 032318 770855 051051 485650 133941 738879 856001 > 8167 [i]