Best Known (33, 63, s)-Nets in Base 27
(33, 63, 178)-Net over F27 — Constructive and digital
Digital (33, 63, 178)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (8, 23, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (10, 40, 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 (8, 23, 84)-net over F27, using
(33, 63, 370)-Net in Base 27 — Constructive
(33, 63, 370)-net in base 27, using
- 5 times m-reduction [i] based on (33, 68, 370)-net in base 27, using
- base change [i] based on digital (16, 51, 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, 51, 370)-net over F81, using
(33, 63, 629)-Net over F27 — Digital
Digital (33, 63, 629)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2763, 629, F27, 30) (dual of [629, 566, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2763, 749, F27, 30) (dual of [749, 686, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(21) [i] based on
- 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(2743, 729, F27, 22) (dual of [729, 686, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(277, 20, F27, 7) (dual of [20, 13, 8]-code or 20-arc in PG(6,27)), using
- discarding factors / shortening the dual code based on linear OA(277, 27, F27, 7) (dual of [27, 20, 8]-code or 27-arc in PG(6,27)), using
- Reed–Solomon code RS(20,27) [i]
- discarding factors / shortening the dual code based on linear OA(277, 27, F27, 7) (dual of [27, 20, 8]-code or 27-arc in PG(6,27)), using
- construction X applied to Ce(29) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(2763, 749, F27, 30) (dual of [749, 686, 31]-code), using
(33, 63, 253809)-Net in Base 27 — Upper bound on s
There is no (33, 63, 253810)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 499429 372016 119350 666793 732552 000934 591372 994872 119129 081332 025011 777882 146800 479845 269385 > 2763 [i]