Best Known (133−55, 133, s)-Nets in Base 3
(133−55, 133, 80)-Net over F3 — Constructive and digital
Digital (78, 133, 80)-net over F3, using
- 7 times m-reduction [i] based on digital (78, 140, 80)-net over F3, using
- trace code for nets [i] based on digital (8, 70, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- trace code for nets [i] based on digital (8, 70, 40)-net over F9, using
(133−55, 133, 121)-Net over F3 — Digital
Digital (78, 133, 121)-net over F3, using
(133−55, 133, 1148)-Net in Base 3 — Upper bound on s
There is no (78, 133, 1149)-net in base 3, because
- 1 times m-reduction [i] would yield (78, 132, 1149)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 964 666247 823397 280861 419246 362522 028806 047714 844693 455250 164331 > 3132 [i]