Best Known (110−25, 110, s)-Nets in Base 27
(110−25, 110, 44325)-Net over F27 — Constructive and digital
Digital (85, 110, 44325)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- digital (72, 97, 44287)-net over F27, using
- net defined by OOA [i] based on linear OOA(2797, 44287, F27, 25, 25) (dual of [(44287, 25), 1107078, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2797, 531445, F27, 25) (dual of [531445, 531348, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(2797, 531441, F27, 25) (dual of [531441, 531344, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2793, 531441, F27, 24) (dual of [531441, 531348, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(24) ⊂ Ce(23) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(2797, 531445, F27, 25) (dual of [531445, 531348, 26]-code), using
- net defined by OOA [i] based on linear OOA(2797, 44287, F27, 25, 25) (dual of [(44287, 25), 1107078, 26]-NRT-code), using
- digital (1, 13, 38)-net over F27, using
(110−25, 110, 1370284)-Net over F27 — Digital
Digital (85, 110, 1370284)-net over F27, using
(110−25, 110, large)-Net in Base 27 — Upper bound on s
There is no (85, 110, large)-net in base 27, because
- 23 times m-reduction [i] would yield (85, 87, large)-net in base 27, but