Best Known (34−29, 34, s)-Nets in Base 7
(34−29, 34, 13)-Net over F7 — Constructive and digital
Digital (5, 34, 13)-net over F7, using
- net from sequence [i] based on digital (5, 12)-sequence over F7, using
(34−29, 34, 24)-Net over F7 — Digital
Digital (5, 34, 24)-net over F7, using
- t-expansion [i] based on digital (4, 34, 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
(34−29, 34, 57)-Net over F7 — Upper bound on s (digital)
There is no digital (5, 34, 58)-net over F7, because
- 1 times m-reduction [i] would yield digital (5, 33, 58)-net over F7, but
- 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
- extracting embedded orthogonal array [i] would yield linear OA(733, 58, F7, 28) (dual of [58, 25, 29]-code), but
(34−29, 34, 75)-Net in Base 7 — Upper bound on s
There is no (5, 34, 76)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(734, 76, S7, 29), but
- the linear programming bound shows that M ≥ 1104 767111 432500 930376 966448 543772 525848 489323 448063 923277 690120 / 18930 999823 588323 231167 214657 916817 > 734 [i]