Best Known (79, 79+18, s)-Nets in Base 27
(79, 79+18, 932115)-Net over F27 — Constructive and digital
Digital (79, 97, 932115)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-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 (2, 11, 48)-net over F27, using
(79, 79+18, large)-Net over F27 — Digital
Digital (79, 97, large)-net over F27, using
- 271 times duplication [i] based on digital (78, 96, large)-net over F27, using
- t-expansion [i] based on digital (76, 96, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2796, large, F27, 20) (dual of [large, large−96, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2796, large, F27, 20) (dual of [large, large−96, 21]-code), using
- t-expansion [i] based on digital (76, 96, large)-net over F27, using
(79, 79+18, large)-Net in Base 27 — Upper bound on s
There is no (79, 97, large)-net in base 27, because
- 16 times m-reduction [i] would yield (79, 81, large)-net in base 27, but