Best Known (64, 64+18, s)-Nets in Base 27
(64, 64+18, 59113)-Net over F27 — Constructive and digital
Digital (64, 82, 59113)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 13, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (51, 69, 59049)-net over F27, using
- net defined by OOA [i] based on linear OOA(2769, 59049, F27, 18, 18) (dual of [(59049, 18), 1062813, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2769, 531441, F27, 18) (dual of [531441, 531372, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- OA 9-folding and stacking [i] based on linear OA(2769, 531441, F27, 18) (dual of [531441, 531372, 19]-code), using
- net defined by OOA [i] based on linear OOA(2769, 59049, F27, 18, 18) (dual of [(59049, 18), 1062813, 19]-NRT-code), using
- digital (4, 13, 64)-net over F27, using
(64, 64+18, 59132)-Net in Base 27 — Constructive
(64, 82, 59132)-net in base 27, using
- (u, u+v)-construction [i] based on
- (3, 12, 82)-net in base 27, using
- base change [i] based on digital (0, 9, 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
- base change [i] based on digital (0, 9, 82)-net over F81, using
- digital (52, 70, 59050)-net over F27, using
- net defined by OOA [i] based on linear OOA(2770, 59050, F27, 18, 18) (dual of [(59050, 18), 1062830, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2770, 531450, F27, 18) (dual of [531450, 531380, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(2769, 531441, F27, 18) (dual of [531441, 531372, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- 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]
- linear OA(271, 9, F27, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- OA 9-folding and stacking [i] based on linear OA(2770, 531450, F27, 18) (dual of [531450, 531380, 19]-code), using
- net defined by OOA [i] based on linear OOA(2770, 59050, F27, 18, 18) (dual of [(59050, 18), 1062830, 19]-NRT-code), using
- (3, 12, 82)-net in base 27, using
(64, 64+18, 2214108)-Net over F27 — Digital
Digital (64, 82, 2214108)-net over F27, using
(64, 64+18, large)-Net in Base 27 — Upper bound on s
There is no (64, 82, large)-net in base 27, because
- 16 times m-reduction [i] would yield (64, 66, large)-net in base 27, but