Best Known (91−44, 91, s)-Nets in Base 27
(91−44, 91, 192)-Net over F27 — Constructive and digital
Digital (47, 91, 192)-net over F27, using
- 6 times m-reduction [i] based on digital (47, 97, 192)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (11, 36, 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 (11, 61, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27 (see above)
- digital (11, 36, 96)-net over F27, using
- (u, u+v)-construction [i] based on
(91−44, 91, 370)-Net in Base 27 — Constructive
(47, 91, 370)-net in base 27, using
- t-expansion [i] based on (43, 91, 370)-net in base 27, using
- 17 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 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, 81, 370)-net over F81, using
- 17 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(91−44, 91, 722)-Net over F27 — Digital
Digital (47, 91, 722)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2791, 722, F27, 44) (dual of [722, 631, 45]-code), using
- discarding factors / shortening the dual code based on linear OA(2791, 752, F27, 44) (dual of [752, 661, 45]-code), using
- construction X applied to Ce(43) ⊂ Ce(35) [i] based on
- linear OA(2784, 729, F27, 44) (dual of [729, 645, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- 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(277, 23, F27, 7) (dual of [23, 16, 8]-code or 23-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(43) ⊂ Ce(35) [i] based on
- discarding factors / shortening the dual code based on linear OA(2791, 752, F27, 44) (dual of [752, 661, 45]-code), using
(91−44, 91, 290070)-Net in Base 27 — Upper bound on s
There is no (47, 91, 290071)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 17952 115924 018074 089424 253469 086426 685246 878765 023036 868264 714402 037728 627749 536014 396330 476244 931453 634343 143515 485273 802124 706869 > 2791 [i]