Best Known (43, 43+26, s)-Nets in Base 81
(43, 43+26, 740)-Net over F81 — Constructive and digital
Digital (43, 69, 740)-net over F81, using
- 2 times m-reduction [i] based on digital (43, 71, 740)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (13, 27, 937)-net over F81, using
- net defined by OOA [i] based on linear OOA(8127, 937, F81, 14, 14) (dual of [(937, 14), 13091, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(8127, 6559, F81, 14) (dual of [6559, 6532, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(8127, 6559, F81, 14) (dual of [6559, 6532, 15]-code), using
- net defined by OOA [i] based on linear OOA(8127, 937, F81, 14, 14) (dual of [(937, 14), 13091, 15]-NRT-code), using
- digital (16, 44, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- digital (13, 27, 937)-net over F81, using
- (u, u+v)-construction [i] based on
(43, 43+26, 23561)-Net over F81 — Digital
Digital (43, 69, 23561)-net over F81, using
(43, 43+26, large)-Net in Base 81 — Upper bound on s
There is no (43, 69, large)-net in base 81, because
- 24 times m-reduction [i] would yield (43, 45, large)-net in base 81, but