Best Known (46−33, 46, s)-Nets in Base 81
(46−33, 46, 224)-Net over F81 — Constructive and digital
Digital (13, 46, 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
(46−33, 46, 298)-Net over F81 — Digital
Digital (13, 46, 298)-net over F81, using
- t-expansion [i] based on digital (12, 46, 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
(46−33, 46, 19810)-Net in Base 81 — Upper bound on s
There is no (13, 46, 19811)-net in base 81, because
- 1 times m-reduction [i] would yield (13, 45, 19811)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 76 211867 288364 525807 657070 359100 250436 753322 836091 824797 660516 615111 067214 515741 966081 > 8145 [i]