Best Known (27, 27+16, s)-Nets in Base 5
(27, 27+16, 132)-Net over F5 — Constructive and digital
Digital (27, 43, 132)-net over F5, using
- 3 times m-reduction [i] based on digital (27, 46, 132)-net over F5, using
- trace code for nets [i] based on digital (4, 23, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- trace code for nets [i] based on digital (4, 23, 66)-net over F25, using
(27, 27+16, 170)-Net over F5 — Digital
Digital (27, 43, 170)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(543, 170, F5, 16) (dual of [170, 127, 17]-code), using
- 39 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 0, 1, 6 times 0, 1, 10 times 0, 1, 14 times 0) [i] based on linear OA(537, 125, F5, 16) (dual of [125, 88, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- 39 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 0, 1, 6 times 0, 1, 10 times 0, 1, 14 times 0) [i] based on linear OA(537, 125, F5, 16) (dual of [125, 88, 17]-code), using
(27, 27+16, 5372)-Net in Base 5 — Upper bound on s
There is no (27, 43, 5373)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 138275 596992 471420 588813 596385 > 543 [i]