Best Known (69−16, 69, s)-Nets in Base 27
(69−16, 69, 66458)-Net over F27 — Constructive and digital
Digital (53, 69, 66458)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- digital (45, 61, 66430)-net over F27, using
- net defined by OOA [i] based on linear OOA(2761, 66430, F27, 16, 16) (dual of [(66430, 16), 1062819, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2761, 531440, F27, 16) (dual of [531440, 531379, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2761, 531441, F27, 16) (dual of [531441, 531380, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2761, 531441, F27, 16) (dual of [531441, 531380, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2761, 531440, F27, 16) (dual of [531440, 531379, 17]-code), using
- net defined by OOA [i] based on linear OOA(2761, 66430, F27, 16, 16) (dual of [(66430, 16), 1062819, 17]-NRT-code), using
- digital (0, 8, 28)-net over F27, using
(69−16, 69, 948571)-Net over F27 — Digital
Digital (53, 69, 948571)-net over F27, using
(69−16, 69, large)-Net in Base 27 — Upper bound on s
There is no (53, 69, large)-net in base 27, because
- 14 times m-reduction [i] would yield (53, 55, large)-net in base 27, but