Best Known (35−16, 35, s)-Nets in Base 27
(35−16, 35, 146)-Net over F27 — Constructive and digital
Digital (19, 35, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (7, 23, 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 (4, 12, 64)-net over F27, using
(35−16, 35, 200)-Net in Base 27 — Constructive
(19, 35, 200)-net in base 27, using
- 1 times m-reduction [i] based on (19, 36, 200)-net in base 27, using
- base change [i] based on digital (10, 27, 200)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 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, 18, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81 (see above)
- digital (1, 9, 100)-net over F81, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (10, 27, 200)-net over F81, using
(35−16, 35, 690)-Net over F27 — Digital
Digital (19, 35, 690)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2735, 690, F27, 16) (dual of [690, 655, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2735, 743, F27, 16) (dual of [743, 708, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(2731, 729, F27, 16) (dual of [729, 698, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2721, 729, F27, 11) (dual of [729, 708, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(15) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(2735, 743, F27, 16) (dual of [743, 708, 17]-code), using
(35−16, 35, 264805)-Net in Base 27 — Upper bound on s
There is no (19, 35, 264806)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 125 238768 220997 631397 666065 711151 709182 901535 458769 > 2735 [i]