Best Known (215−101, 215, s)-Nets in Base 3
(215−101, 215, 76)-Net over F3 — Constructive and digital
Digital (114, 215, 76)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (32, 82, 38)-net over F3, using
- net from sequence [i] based on digital (32, 37)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 32 and N(F) ≥ 38, using
- net from sequence [i] based on digital (32, 37)-sequence over F3, using
- digital (32, 133, 38)-net over F3, using
- net from sequence [i] based on digital (32, 37)-sequence over F3 (see above)
- digital (32, 82, 38)-net over F3, using
(215−101, 215, 127)-Net over F3 — Digital
Digital (114, 215, 127)-net over F3, using
(215−101, 215, 1024)-Net in Base 3 — Upper bound on s
There is no (114, 215, 1025)-net in base 3, because
- 1 times m-reduction [i] would yield (114, 214, 1025)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1 288178 542995 743492 406081 267705 951528 439910 869634 084746 304503 181605 805681 635427 030245 922699 614210 591689 > 3214 [i]