Best Known (63, 63+69, s)-Nets in Base 3
(63, 63+69, 52)-Net over F3 — Constructive and digital
Digital (63, 132, 52)-net over F3, using
- 1 times m-reduction [i] based on digital (63, 133, 52)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (13, 48, 24)-net over F3, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 13 and N(F) ≥ 24, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- digital (15, 85, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- digital (13, 48, 24)-net over F3, using
- (u, u+v)-construction [i] based on
(63, 63+69, 64)-Net over F3 — Digital
Digital (63, 132, 64)-net over F3, using
- t-expansion [i] based on digital (49, 132, 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
(63, 63+69, 433)-Net in Base 3 — Upper bound on s
There is no (63, 132, 434)-net in base 3, because
- 1 times m-reduction [i] would yield (63, 131, 434)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 321 272273 235375 866082 571074 580659 341621 084197 100238 536977 523445 > 3131 [i]