Best Known (1, 1+32, s)-Nets in Base 25
(1, 1+32, 27)-Net over F25 — Constructive and digital
Digital (1, 33, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
(1, 1+32, 36)-Net over F25 — Digital
Digital (1, 33, 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
(1, 1+32, 74)-Net over F25 — Upper bound on s (digital)
There is no digital (1, 33, 75)-net over F25, because
- 7 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
(1, 1+32, 104)-Net in Base 25 — Upper bound on s
There is no (1, 33, 105)-net in base 25, because
- extracting embedded orthogonal array [i] would yield OA(2533, 105, S25, 32), but
- the linear programming bound shows that M ≥ 17445 219531 106448 407342 668360 797688 364982 604980 468750 / 1 268759 > 2533 [i]