Best Known (203−61, 203, s)-Nets in Base 3
(203−61, 203, 228)-Net over F3 — Constructive and digital
Digital (142, 203, 228)-net over F3, using
- 1 times m-reduction [i] based on digital (142, 204, 228)-net over F3, using
- trace code for nets [i] based on digital (6, 68, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- trace code for nets [i] based on digital (6, 68, 76)-net over F27, using
(203−61, 203, 446)-Net over F3 — Digital
Digital (142, 203, 446)-net over F3, using
(203−61, 203, 9796)-Net in Base 3 — Upper bound on s
There is no (142, 203, 9797)-net in base 3, because
- 1 times m-reduction [i] would yield (142, 202, 9797)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 2 394178 671821 297403 402310 814535 896881 050707 137847 319430 011657 114481 918445 138497 967623 628195 555105 > 3202 [i]