Best Known (37, 73, s)-Nets in Base 27
(37, 73, 182)-Net over F27 — Constructive and digital
Digital (37, 73, 182)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 27, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (10, 46, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (9, 27, 88)-net over F27, using
(37, 73, 370)-Net in Base 27 — Constructive
(37, 73, 370)-net in base 27, using
- 11 times m-reduction [i] based on (37, 84, 370)-net in base 27, using
- base change [i] based on digital (16, 63, 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, 63, 370)-net over F81, using
(37, 73, 544)-Net over F27 — Digital
Digital (37, 73, 544)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2773, 544, F27, 36) (dual of [544, 471, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(2773, 746, F27, 36) (dual of [746, 673, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(29) [i] based on
- linear OA(2768, 729, F27, 36) (dual of [729, 661, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2756, 729, F27, 30) (dual of [729, 673, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(275, 17, F27, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,27)), using
- discarding factors / shortening the dual code based on linear OA(275, 27, F27, 5) (dual of [27, 22, 6]-code or 27-arc in PG(4,27)), using
- Reed–Solomon code RS(22,27) [i]
- discarding factors / shortening the dual code based on linear OA(275, 27, F27, 5) (dual of [27, 22, 6]-code or 27-arc in PG(4,27)), using
- construction X applied to Ce(35) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(2773, 746, F27, 36) (dual of [746, 673, 37]-code), using
(37, 73, 185400)-Net in Base 27 — Upper bound on s
There is no (37, 73, 185401)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 308 733756 490679 809377 324877 830835 028056 781269 038913 927209 802792 477784 410949 137601 441543 562532 160926 715209 > 2773 [i]