Best Known (46−16, 46, s)-Nets in Base 8
(46−16, 46, 354)-Net over F8 — Constructive and digital
Digital (30, 46, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 23, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
(46−16, 46, 516)-Net in Base 8 — Constructive
(30, 46, 516)-net in base 8, using
- trace code for nets [i] based on (7, 23, 258)-net in base 64, using
- 1 times m-reduction [i] based on (7, 24, 258)-net in base 64, using
- base change [i] based on digital (1, 18, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 18, 258)-net over F256, using
- 1 times m-reduction [i] based on (7, 24, 258)-net in base 64, using
(46−16, 46, 571)-Net over F8 — Digital
Digital (30, 46, 571)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(846, 571, F8, 16) (dual of [571, 525, 17]-code), using
- 55 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 14 times 0, 1, 34 times 0) [i] based on linear OA(842, 512, F8, 16) (dual of [512, 470, 17]-code), using
- 1 times truncation [i] based on linear OA(843, 513, F8, 17) (dual of [513, 470, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 513 | 86−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(843, 513, F8, 17) (dual of [513, 470, 18]-code), using
- 55 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 14 times 0, 1, 34 times 0) [i] based on linear OA(842, 512, F8, 16) (dual of [512, 470, 17]-code), using
(46−16, 46, 578)-Net in Base 8
(30, 46, 578)-net in base 8, using
- trace code for nets [i] based on (7, 23, 289)-net in base 64, using
- 1 times m-reduction [i] based on (7, 24, 289)-net in base 64, using
- base change [i] based on digital (1, 18, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- base change [i] based on digital (1, 18, 289)-net over F256, using
- 1 times m-reduction [i] based on (7, 24, 289)-net in base 64, using
(46−16, 46, 83817)-Net in Base 8 — Upper bound on s
There is no (30, 46, 83818)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 348461 330351 106481 710980 903634 709341 831949 > 846 [i]