Best Known (34−33, 34, s)-Nets in Base 25
(34−33, 34, 27)-Net over F25 — Constructive and digital
Digital (1, 34, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
(34−33, 34, 36)-Net over F25 — Digital
Digital (1, 34, 36)-net over F25, using
- net from sequence [i] based on digital (1, 35)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 1 and N(F) ≥ 36, using
(34−33, 34, 74)-Net over F25 — Upper bound on s (digital)
There is no digital (1, 34, 75)-net over F25, because
- 8 times m-reduction [i] would yield digital (1, 26, 75)-net over F25, but
- extracting embedded orthogonal array [i] would yield linear OA(2526, 75, F25, 25) (dual of [75, 49, 26]-code), but
- dual of a near-MDS code is again a near-MDS code [i] would yield linear OA(2549, 75, F25, 48) (dual of [75, 26, 49]-code), but
- discarding factors / shortening the dual code would yield linear OA(2549, 52, F25, 48) (dual of [52, 3, 49]-code), but
- dual of a near-MDS code is again a near-MDS code [i] would yield linear OA(2549, 75, F25, 48) (dual of [75, 26, 49]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(2526, 75, F25, 25) (dual of [75, 49, 26]-code), but
(34−33, 34, 102)-Net in Base 25 — Upper bound on s
There is no (1, 34, 103)-net in base 25, because
- extracting embedded orthogonal array [i] would yield OA(2534, 103, S25, 33), but
- the linear programming bound shows that M ≥ 2 685149 330531 114153 508553 954452 509060 502052 307128 906250 / 7 688413 > 2534 [i]