Best Known (93, 109, s)-Nets in Base 27
(93, 109, 1181464)-Net over F27 — Constructive and digital
Digital (93, 109, 1181464)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (25, 33, 132889)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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 (21, 29, 132861)-net over F27, using
- net defined by OOA [i] based on linear OOA(2729, 132861, F27, 8, 8) (dual of [(132861, 8), 1062859, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2729, 531444, F27, 8) (dual of [531444, 531415, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2729, 531445, F27, 8) (dual of [531445, 531416, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(2729, 531441, F27, 8) (dual of [531441, 531412, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2725, 531441, F27, 7) (dual of [531441, 531416, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(2729, 531445, F27, 8) (dual of [531445, 531416, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(2729, 531444, F27, 8) (dual of [531444, 531415, 9]-code), using
- net defined by OOA [i] based on linear OOA(2729, 132861, F27, 8, 8) (dual of [(132861, 8), 1062859, 9]-NRT-code), using
- digital (0, 4, 28)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (60, 76, 1048575)-net over F27, using
- net defined by OOA [i] based on linear OOA(2776, 1048575, F27, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2776, 8388600, F27, 16) (dual of [8388600, 8388524, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2776, large, F27, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2776, large, F27, 16) (dual of [large, large−76, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2776, 8388600, F27, 16) (dual of [8388600, 8388524, 17]-code), using
- net defined by OOA [i] based on linear OOA(2776, 1048575, F27, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- digital (25, 33, 132889)-net over F27, using
(93, 109, large)-Net over F27 — Digital
Digital (93, 109, large)-net over F27, using
- 273 times duplication [i] based on digital (90, 106, large)-net over F27, using
- t-expansion [i] based on digital (84, 106, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(27106, large, F27, 22) (dual of [large, large−106, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(27106, large, F27, 22) (dual of [large, large−106, 23]-code), using
- t-expansion [i] based on digital (84, 106, large)-net over F27, using
(93, 109, large)-Net in Base 27 — Upper bound on s
There is no (93, 109, large)-net in base 27, because
- 14 times m-reduction [i] would yield (93, 95, large)-net in base 27, but