Best Known (32, 45, s)-Nets in Base 81
(32, 45, 88689)-Net over F81 — Constructive and digital
Digital (32, 45, 88689)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 8, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- digital (24, 37, 88573)-net over F81, using
- net defined by OOA [i] based on linear OOA(8137, 88573, F81, 13, 13) (dual of [(88573, 13), 1151412, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(8137, 531439, F81, 13) (dual of [531439, 531402, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, 531441, F81, 13) (dual of [531441, 531404, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(8137, 531441, F81, 13) (dual of [531441, 531404, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(8137, 531439, F81, 13) (dual of [531439, 531402, 14]-code), using
- net defined by OOA [i] based on linear OOA(8137, 88573, F81, 13, 13) (dual of [(88573, 13), 1151412, 14]-NRT-code), using
- digital (2, 8, 116)-net over F81, using
(32, 45, 948622)-Net over F81 — Digital
Digital (32, 45, 948622)-net over F81, using
(32, 45, large)-Net in Base 81 — Upper bound on s
There is no (32, 45, large)-net in base 81, because
- 11 times m-reduction [i] would yield (32, 34, large)-net in base 81, but