Best Known (5, 5+28, s)-Nets in Base 7
(5, 5+28, 13)-Net over F7 — Constructive and digital
Digital (5, 33, 13)-net over F7, using
- net from sequence [i] based on digital (5, 12)-sequence over F7, using
(5, 5+28, 24)-Net over F7 — Digital
Digital (5, 33, 24)-net over F7, using
- t-expansion [i] based on digital (4, 33, 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
(5, 5+28, 57)-Net over F7 — Upper bound on s (digital)
There is no digital (5, 33, 58)-net over F7, because
- extracting embedded orthogonal array [i] would yield linear OA(733, 58, F7, 28) (dual of [58, 25, 29]-code), but
- residual code [i] would yield OA(75, 29, S7, 4), but
- the linear programming bound shows that M ≥ 3 384381 / 197 > 75 [i]
- residual code [i] would yield OA(75, 29, S7, 4), but
(5, 5+28, 77)-Net in Base 7 — Upper bound on s
There is no (5, 33, 78)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(733, 78, S7, 28), but
- the linear programming bound shows that M ≥ 789 366853 161980 825054 272728 274257 348494 169454 383681 114625 / 91590 861679 687045 735081 101566 > 733 [i]