Best Known (67−18, 67, s)-Nets in Base 81
(67−18, 67, 59249)-Net over F81 — Constructive and digital
Digital (49, 67, 59249)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (6, 15, 200)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- digital (1, 10, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81 (see above)
- digital (1, 5, 100)-net over F81, using
- (u, u+v)-construction [i] based on
- 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 (6, 15, 200)-net over F81, using
(67−18, 67, 2982172)-Net over F81 — Digital
Digital (49, 67, 2982172)-net over F81, using
(67−18, 67, large)-Net in Base 81 — Upper bound on s
There is no (49, 67, large)-net in base 81, because
- 16 times m-reduction [i] would yield (49, 51, large)-net in base 81, but