Best Known (36, 36+16, s)-Nets in Base 5
(36, 36+16, 252)-Net over F5 — Constructive and digital
Digital (36, 52, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 26, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(36, 36+16, 523)-Net over F5 — Digital
Digital (36, 52, 523)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(552, 523, F5, 16) (dual of [523, 471, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(552, 624, F5, 16) (dual of [624, 572, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(552, 624, F5, 16) (dual of [624, 572, 17]-code), using
(36, 36+16, 32874)-Net in Base 5 — Upper bound on s
There is no (36, 52, 32875)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 2 220581 283889 165447 753310 110654 936801 > 552 [i]