Best Known (99−30, 99, s)-Nets in Base 5
(99−30, 99, 296)-Net over F5 — Constructive and digital
Digital (69, 99, 296)-net over F5, using
- 1 times m-reduction [i] based on digital (69, 100, 296)-net over F5, using
- trace code for nets [i] based on digital (19, 50, 148)-net over F25, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 148, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
- trace code for nets [i] based on digital (19, 50, 148)-net over F25, using
(99−30, 99, 725)-Net over F5 — Digital
Digital (69, 99, 725)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(599, 725, F5, 30) (dual of [725, 626, 31]-code), using
- 96 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 6 times 0, 1, 19 times 0, 1, 30 times 0, 1, 35 times 0) [i] based on linear OA(594, 624, F5, 30) (dual of [624, 530, 31]-code), using
- the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 96 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 6 times 0, 1, 19 times 0, 1, 30 times 0, 1, 35 times 0) [i] based on linear OA(594, 624, F5, 30) (dual of [624, 530, 31]-code), using
(99−30, 99, 65892)-Net in Base 5 — Upper bound on s
There is no (69, 99, 65893)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1577 800549 436294 016844 917884 340230 921452 443039 456670 826711 572138 231389 > 599 [i]