Best Known (13, 72, s)-Nets in Base 81
(13, 72, 224)-Net over F81 — Constructive and digital
Digital (13, 72, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
(13, 72, 298)-Net over F81 — Digital
Digital (13, 72, 298)-net over F81, using
- t-expansion [i] based on digital (12, 72, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
(13, 72, 6848)-Net in Base 81 — Upper bound on s
There is no (13, 72, 6849)-net in base 81, because
- 1 times m-reduction [i] would yield (13, 71, 6849)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 3181 495108 307032 009136 168241 425083 134315 324474 897346 203909 705473 414206 811676 633701 105433 552439 822336 690693 445041 460869 693738 131375 569681 > 8171 [i]