Best Known (27, 27+18, s)-Nets in Base 81
(27, 27+18, 829)-Net over F81 — Constructive and digital
Digital (27, 45, 829)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 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 (17, 35, 729)-net over F81, using
- net defined by OOA [i] based on linear OOA(8135, 729, F81, 18, 18) (dual of [(729, 18), 13087, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- OA 9-folding and stacking [i] based on linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using
- net defined by OOA [i] based on linear OOA(8135, 729, F81, 18, 18) (dual of [(729, 18), 13087, 19]-NRT-code), using
- digital (1, 10, 100)-net over F81, using
(27, 27+18, 10118)-Net over F81 — Digital
Digital (27, 45, 10118)-net over F81, using
(27, 27+18, large)-Net in Base 81 — Upper bound on s
There is no (27, 45, large)-net in base 81, because
- 16 times m-reduction [i] would yield (27, 29, large)-net in base 81, but