Best Known (33, 47, s)-Nets in Base 5
(33, 47, 208)-Net over F5 — Constructive and digital
Digital (33, 47, 208)-net over F5, using
- 1 times m-reduction [i] based on 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
- trace code for nets [i] based on digital (9, 24, 104)-net over F25, using
(33, 47, 624)-Net over F5 — Digital
Digital (33, 47, 624)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(547, 624, F5, 14) (dual of [624, 577, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(547, 636, F5, 14) (dual of [636, 589, 15]-code), using
- construction XX applied to Ce(13) ⊂ Ce(11) ⊂ Ce(10) [i] based on
- linear OA(545, 625, F5, 14) (dual of [625, 580, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(537, 625, F5, 12) (dual of [625, 588, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(533, 625, F5, 11) (dual of [625, 592, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(51, 10, F5, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(13) ⊂ Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(547, 636, F5, 14) (dual of [636, 589, 15]-code), using
(33, 47, 41676)-Net in Base 5 — Upper bound on s
There is no (33, 47, 41677)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 710 576759 239969 889191 815595 428125 > 547 [i]