Best Known (6, 6+103, s)-Nets in Base 7
(6, 6+103, 14)-Net over F7 — Constructive and digital
Digital (6, 109, 14)-net over F7, using
- net from sequence [i] based on digital (6, 13)-sequence over F7, using
(6, 6+103, 24)-Net over F7 — Digital
Digital (6, 109, 24)-net over F7, using
- t-expansion [i] based on digital (4, 109, 24)-net over F7, using
- net from sequence [i] based on digital (4, 23)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 4 and N(F) ≥ 24, using
- net from sequence [i] based on digital (4, 23)-sequence over F7, using
(6, 6+103, 50)-Net in Base 7 — Upper bound on s
There is no (6, 109, 51)-net in base 7, because
- 10 times m-reduction [i] would yield (6, 99, 51)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(799, 51, S7, 2, 93), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25 875812 076998 063930 757182 152801 734486 857625 591237 003207 471162 651133 531677 095424 480008 / 47 > 799 [i]
- extracting embedded OOA [i] would yield OOA(799, 51, S7, 2, 93), but