Best Known (131−49, 131, s)-Nets in Base 3
(131−49, 131, 128)-Net over F3 — Constructive and digital
Digital (82, 131, 128)-net over F3, using
- 7 times m-reduction [i] based on digital (82, 138, 128)-net over F3, using
- trace code for nets [i] based on digital (13, 69, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- trace code for nets [i] based on digital (13, 69, 64)-net over F9, using
(131−49, 131, 158)-Net over F3 — Digital
Digital (82, 131, 158)-net over F3, using
(131−49, 131, 1859)-Net in Base 3 — Upper bound on s
There is no (82, 131, 1860)-net in base 3, because
- 1 times m-reduction [i] would yield (82, 130, 1860)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 107 279132 948873 058068 676945 877260 711386 660961 270426 743580 485697 > 3130 [i]