Best Known (46−11, 46, s)-Nets in Base 27
(46−11, 46, 106316)-Net over F27 — Constructive and digital
Digital (35, 46, 106316)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 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 (30, 41, 106288)-net over F27, using
- net defined by OOA [i] based on linear OOA(2741, 106288, F27, 11, 11) (dual of [(106288, 11), 1169127, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2741, 531441, F27, 11) (dual of [531441, 531400, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(2741, 531441, F27, 11) (dual of [531441, 531400, 12]-code), using
- net defined by OOA [i] based on linear OOA(2741, 106288, F27, 11, 11) (dual of [(106288, 11), 1169127, 12]-NRT-code), using
- digital (0, 5, 28)-net over F27, using
(46−11, 46, 668774)-Net over F27 — Digital
Digital (35, 46, 668774)-net over F27, using
(46−11, 46, large)-Net in Base 27 — Upper bound on s
There is no (35, 46, large)-net in base 27, because
- 9 times m-reduction [i] would yield (35, 37, large)-net in base 27, but