Best Known (233−67, 233, s)-Nets in Base 3
(233−67, 233, 282)-Net over F3 — Constructive and digital
Digital (166, 233, 282)-net over F3, using
- 1 times m-reduction [i] based on digital (166, 234, 282)-net over F3, using
- trace code for nets [i] based on digital (10, 78, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- trace code for nets [i] based on digital (10, 78, 94)-net over F27, using
(233−67, 233, 581)-Net over F3 — Digital
Digital (166, 233, 581)-net over F3, using
(233−67, 233, 14848)-Net in Base 3 — Upper bound on s
There is no (166, 233, 14849)-net in base 3, because
- 1 times m-reduction [i] would yield (166, 232, 14849)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 492 739106 032691 059781 950598 456759 484238 730799 703707 836686 159603 743815 607073 800645 043899 316991 310514 095714 774915 > 3232 [i]