Best Known (28, 28+41, s)-Nets in Base 81
(28, 28+41, 370)-Net over F81 — Constructive and digital
Digital (28, 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
(28, 28+41, 500)-Net over F81 — Digital
Digital (28, 69, 500)-net over F81, using
- t-expansion [i] based on digital (26, 69, 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
- net from sequence [i] based on digital (26, 499)-sequence over F81, using
(28, 28+41, 319927)-Net in Base 81 — Upper bound on s
There is no (28, 69, 319928)-net in base 81, because
- 1 times m-reduction [i] would yield (28, 68, 319928)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 5983 907153 855548 176239 724267 764808 634219 409701 728839 234089 889364 654014 944075 880739 394360 764424 378436 378657 376435 636152 583715 980801 > 8168 [i]