Best Known (55−22, 55, s)-Nets in Base 81
(55−22, 55, 696)-Net over F81 — Constructive and digital
Digital (33, 55, 696)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 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 (21, 43, 596)-net over F81, using
- net defined by OOA [i] based on linear OOA(8143, 596, F81, 22, 22) (dual of [(596, 22), 13069, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8143, 6556, F81, 22) (dual of [6556, 6513, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8143, 6556, F81, 22) (dual of [6556, 6513, 23]-code), using
- net defined by OOA [i] based on linear OOA(8143, 596, F81, 22, 22) (dual of [(596, 22), 13069, 23]-NRT-code), using
- digital (1, 12, 100)-net over F81, using
(55−22, 55, 10820)-Net over F81 — Digital
Digital (33, 55, 10820)-net over F81, using
(55−22, 55, large)-Net in Base 81 — Upper bound on s
There is no (33, 55, large)-net in base 81, because
- 20 times m-reduction [i] would yield (33, 35, large)-net in base 81, but