Best Known (52−15, 52, s)-Nets in Base 81
(52−15, 52, 76036)-Net over F81 — Constructive and digital
Digital (37, 52, 76036)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 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 (28, 43, 75920)-net over F81, using
- net defined by OOA [i] based on linear OOA(8143, 75920, F81, 15, 15) (dual of [(75920, 15), 1138757, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(8143, 531441, F81, 15) (dual of [531441, 531398, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(8143, 531441, F81, 15) (dual of [531441, 531398, 16]-code), using
- net defined by OOA [i] based on linear OOA(8143, 75920, F81, 15, 15) (dual of [(75920, 15), 1138757, 16]-NRT-code), using
- digital (2, 9, 116)-net over F81, using
(52−15, 52, 926893)-Net over F81 — Digital
Digital (37, 52, 926893)-net over F81, using
(52−15, 52, large)-Net in Base 81 — Upper bound on s
There is no (37, 52, large)-net in base 81, because
- 13 times m-reduction [i] would yield (37, 39, large)-net in base 81, but