Best Known (34, 34+27, s)-Nets in Base 27
(34, 34+27, 192)-Net over F27 — Constructive and digital
Digital (34, 61, 192)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (10, 23, 96)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 8, 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 (2, 15, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27 (see above)
- digital (2, 8, 48)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (11, 38, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- digital (10, 23, 96)-net over F27, using
(34, 34+27, 370)-Net in Base 27 — Constructive
(34, 61, 370)-net in base 27, using
- 11 times m-reduction [i] based on (34, 72, 370)-net in base 27, using
- base change [i] based on digital (16, 54, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 54, 370)-net over F81, using
(34, 34+27, 943)-Net over F27 — Digital
Digital (34, 61, 943)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2761, 943, F27, 27) (dual of [943, 882, 28]-code), using
- 206 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 14 times 0, 1, 30 times 0, 1, 58 times 0, 1, 92 times 0) [i] based on linear OA(2752, 728, F27, 27) (dual of [728, 676, 28]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 206 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 14 times 0, 1, 30 times 0, 1, 58 times 0, 1, 92 times 0) [i] based on linear OA(2752, 728, F27, 27) (dual of [728, 676, 28]-code), using
(34, 34+27, 880488)-Net in Base 27 — Upper bound on s
There is no (34, 61, 880489)-net in base 27, because
- 1 times m-reduction [i] would yield (34, 60, 880489)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 76 177380 876244 388794 532719 728819 926746 014688 858480 339519 570325 182477 051382 525481 555099 > 2760 [i]