Best Known (83, 83+18, s)-Nets in Base 27
(83, 83+18, 932143)-Net over F27 — Constructive and digital
Digital (83, 101, 932143)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 15, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (68, 86, 932067)-net over F27, using
- net defined by OOA [i] based on linear OOA(2786, 932067, F27, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2786, large, F27, 18) (dual of [large, large−86, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(2786, large, F27, 18) (dual of [large, large−86, 19]-code), using
- net defined by OOA [i] based on linear OOA(2786, 932067, F27, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- digital (6, 15, 76)-net over F27, using
(83, 83+18, 932183)-Net in Base 27 — Constructive
(83, 101, 932183)-net in base 27, using
- (u, u+v)-construction [i] based on
- (6, 15, 116)-net in base 27, using
- 1 times m-reduction [i] based on (6, 16, 116)-net in base 27, using
- base change [i] based on digital (2, 12, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 12, 116)-net over F81, using
- 1 times m-reduction [i] based on (6, 16, 116)-net in base 27, using
- digital (68, 86, 932067)-net over F27, using
- net defined by OOA [i] based on linear OOA(2786, 932067, F27, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2786, large, F27, 18) (dual of [large, large−86, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(2786, large, F27, 18) (dual of [large, large−86, 19]-code), using
- net defined by OOA [i] based on linear OOA(2786, 932067, F27, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- (6, 15, 116)-net in base 27, using
(83, 83+18, large)-Net over F27 — Digital
Digital (83, 101, large)-net over F27, using
- t-expansion [i] based on digital (80, 101, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(27101, large, F27, 21) (dual of [large, large−101, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(27101, large, F27, 21) (dual of [large, large−101, 22]-code), using
(83, 83+18, large)-Net in Base 27 — Upper bound on s
There is no (83, 101, large)-net in base 27, because
- 16 times m-reduction [i] would yield (83, 85, large)-net in base 27, but