Best Known (65, 65+77, s)-Nets in Base 3
(65, 65+77, 48)-Net over F3 — Constructive and digital
Digital (65, 142, 48)-net over F3, using
- t-expansion [i] based on digital (45, 142, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(65, 65+77, 64)-Net over F3 — Digital
Digital (65, 142, 64)-net over F3, using
- t-expansion [i] based on digital (49, 142, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(65, 65+77, 406)-Net in Base 3 — Upper bound on s
There is no (65, 142, 407)-net in base 3, because
- 1 times m-reduction [i] would yield (65, 141, 407)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 19 619525 591669 147977 468107 341619 487029 635675 602456 567958 489905 776165 > 3141 [i]