Best Known (43−20, 43, s)-Nets in Base 27
(43−20, 43, 158)-Net over F27 — Constructive and digital
Digital (23, 43, 158)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 16, 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 (7, 27, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (6, 16, 76)-net over F27, using
(43−20, 43, 200)-Net in Base 27 — Constructive
(23, 43, 200)-net in base 27, using
- 1 times m-reduction [i] based on (23, 44, 200)-net in base 27, using
- base change [i] based on digital (12, 33, 200)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 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
- digital (1, 22, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81 (see above)
- digital (1, 11, 100)-net over F81, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (12, 33, 200)-net over F81, using
(43−20, 43, 627)-Net over F27 — Digital
Digital (23, 43, 627)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2743, 627, F27, 20) (dual of [627, 584, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2743, 743, F27, 20) (dual of [743, 700, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- linear OA(2739, 729, F27, 20) (dual of [729, 690, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2729, 729, F27, 15) (dual of [729, 700, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(274, 14, F27, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,27)), using
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
- Reed–Solomon code RS(23,27) [i]
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(2743, 743, F27, 20) (dual of [743, 700, 21]-code), using
(43−20, 43, 248804)-Net in Base 27 — Upper bound on s
There is no (23, 43, 248805)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 35 370951 660954 503650 535165 907019 684627 985858 422432 569827 777089 > 2743 [i]