Best Known (50, 50+16, s)-Nets in Base 3
(50, 50+16, 328)-Net over F3 — Constructive and digital
Digital (50, 66, 328)-net over F3, using
- 32 times duplication [i] based on digital (48, 64, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 16, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 16, 82)-net over F81, using
(50, 50+16, 484)-Net over F3 — Digital
Digital (50, 66, 484)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(366, 484, F3, 16) (dual of [484, 418, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(366, 728, F3, 16) (dual of [728, 662, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(366, 728, F3, 16) (dual of [728, 662, 17]-code), using
(50, 50+16, 16244)-Net in Base 3 — Upper bound on s
There is no (50, 66, 16245)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 30 908685 024917 993199 502505 494369 > 366 [i]