Best Known (63−18, 63, s)-Nets in Base 81
(63−18, 63, 59165)-Net over F81 — Constructive and digital
Digital (45, 63, 59165)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 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 (34, 52, 59049)-net over F81, using
- net defined by OOA [i] based on linear OOA(8152, 59049, F81, 18, 18) (dual of [(59049, 18), 1062830, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(8152, 531441, F81, 18) (dual of [531441, 531389, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- OA 9-folding and stacking [i] based on linear OA(8152, 531441, F81, 18) (dual of [531441, 531389, 19]-code), using
- net defined by OOA [i] based on linear OOA(8152, 59049, F81, 18, 18) (dual of [(59049, 18), 1062830, 19]-NRT-code), using
- digital (2, 11, 116)-net over F81, using
(63−18, 63, 1060424)-Net over F81 — Digital
Digital (45, 63, 1060424)-net over F81, using
(63−18, 63, large)-Net in Base 81 — Upper bound on s
There is no (45, 63, large)-net in base 81, because
- 16 times m-reduction [i] would yield (45, 47, large)-net in base 81, but