Best Known (33, 33+15, s)-Nets in Base 5
(33, 33+15, 208)-Net over F5 — Constructive and digital
Digital (33, 48, 208)-net over F5, using
- trace code for nets [i] based on digital (9, 24, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
(33, 33+15, 469)-Net over F5 — Digital
Digital (33, 48, 469)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(548, 469, F5, 15) (dual of [469, 421, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(548, 624, F5, 15) (dual of [624, 576, 16]-code), using
- the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(548, 624, F5, 15) (dual of [624, 576, 16]-code), using
(33, 33+15, 41676)-Net in Base 5 — Upper bound on s
There is no (33, 48, 41677)-net in base 5, because
- 1 times m-reduction [i] would yield (33, 47, 41677)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 710 576759 239969 889191 815595 428125 > 547 [i]