Best Known (137, 246, s)-Nets in Base 3
(137, 246, 128)-Net over F3 — Constructive and digital
Digital (137, 246, 128)-net over F3, using
- 2 times m-reduction [i] based on digital (137, 248, 128)-net over F3, using
- trace code for nets [i] based on digital (13, 124, 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, 124, 64)-net over F9, using
(137, 246, 168)-Net over F3 — Digital
Digital (137, 246, 168)-net over F3, using
(137, 246, 1479)-Net in Base 3 — Upper bound on s
There is no (137, 246, 1480)-net in base 3, because
- 1 times m-reduction [i] would yield (137, 245, 1480)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 808 233268 442188 646939 421110 987919 931621 837577 015556 106172 260583 131406 048131 525936 298092 273570 010496 328208 507639 526321 > 3245 [i]