Best Known (82, 100, s)-Nets in Base 27
(82, 100, 932135)-Net over F27 — Constructive and digital
Digital (82, 100, 932135)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (5, 14, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-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 (5, 14, 68)-net over F27, using
(82, 100, 932167)-Net in Base 27 — Constructive
(82, 100, 932167)-net in base 27, using
- (u, u+v)-construction [i] based on
- (5, 14, 100)-net in base 27, using
- 2 times m-reduction [i] based on (5, 16, 100)-net in base 27, using
- base change [i] based on digital (1, 12, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- base change [i] based on digital (1, 12, 100)-net over F81, using
- 2 times m-reduction [i] based on (5, 16, 100)-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
- (5, 14, 100)-net in base 27, using
(82, 100, large)-Net over F27 — Digital
Digital (82, 100, large)-net over F27, using
- t-expansion [i] based on digital (80, 100, large)-net over F27, using
- 1 times m-reduction [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
- 1 times m-reduction [i] based on digital (80, 101, large)-net over F27, using
(82, 100, large)-Net in Base 27 — Upper bound on s
There is no (82, 100, large)-net in base 27, because
- 16 times m-reduction [i] would yield (82, 84, large)-net in base 27, but