Best Known (19, 42, s)-Nets in Base 81
(19, 42, 370)-Net over F81 — Constructive and digital
Digital (19, 42, 370)-net over F81, using
- t-expansion [i] based on digital (16, 42, 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
(19, 42, 509)-Net over F81 — Digital
Digital (19, 42, 509)-net over F81, using
(19, 42, 796829)-Net in Base 81 — Upper bound on s
There is no (19, 42, 796830)-net in base 81, because
- 1 times m-reduction [i] would yield (19, 41, 796830)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 1 769650 005337 713394 964829 777163 777721 808066 149106 270822 287164 604895 144340 090401 > 8141 [i]