Best Known (42, 42+17, s)-Nets in Base 81
(42, 42+17, 66546)-Net over F81 — Constructive and digital
Digital (42, 59, 66546)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 10, 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 (32, 49, 66430)-net over F81, using
- net defined by OOA [i] based on linear OOA(8149, 66430, F81, 17, 17) (dual of [(66430, 17), 1129261, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(8149, 531441, F81, 17) (dual of [531441, 531392, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(8149, 531441, F81, 17) (dual of [531441, 531392, 18]-code), using
- net defined by OOA [i] based on linear OOA(8149, 66430, F81, 17, 17) (dual of [(66430, 17), 1129261, 18]-NRT-code), using
- digital (2, 10, 116)-net over F81, using
(42, 42+17, 926811)-Net over F81 — Digital
Digital (42, 59, 926811)-net over F81, using
(42, 42+17, large)-Net in Base 81 — Upper bound on s
There is no (42, 59, large)-net in base 81, because
- 15 times m-reduction [i] would yield (42, 44, large)-net in base 81, but