Best Known (38, 54, s)-Nets in Base 81
(38, 54, 66512)-Net over F81 — Constructive and digital
Digital (38, 54, 66512)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- digital (30, 46, 66430)-net over F81, using
- net defined by OOA [i] based on linear OOA(8146, 66430, F81, 16, 16) (dual of [(66430, 16), 1062834, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(8146, 531440, F81, 16) (dual of [531440, 531394, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(8146, 531441, F81, 16) (dual of [531441, 531395, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(8146, 531441, F81, 16) (dual of [531441, 531395, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(8146, 531440, F81, 16) (dual of [531440, 531394, 17]-code), using
- net defined by OOA [i] based on linear OOA(8146, 66430, F81, 16, 16) (dual of [(66430, 16), 1062834, 17]-NRT-code), using
- digital (0, 8, 82)-net over F81, using
(38, 54, 595975)-Net over F81 — Digital
Digital (38, 54, 595975)-net over F81, using
(38, 54, large)-Net in Base 81 — Upper bound on s
There is no (38, 54, large)-net in base 81, because
- 14 times m-reduction [i] would yield (38, 40, large)-net in base 81, but