Best Known (46, 75, s)-Nets in Base 8
(46, 75, 354)-Net over F8 — Constructive and digital
Digital (46, 75, 354)-net over F8, using
- 3 times m-reduction [i] based on digital (46, 78, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 39, 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
- trace code for nets [i] based on digital (7, 39, 177)-net over F64, using
(46, 75, 438)-Net over F8 — Digital
Digital (46, 75, 438)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(875, 438, F8, 29) (dual of [438, 363, 30]-code), using
- 362 step Varšamov–Edel lengthening with (ri) = (5, 2, 2, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 19 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 29 times 0) [i] based on linear OA(829, 30, F8, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,8)), using
- dual of repetition code with length 30 [i]
- 362 step Varšamov–Edel lengthening with (ri) = (5, 2, 2, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 19 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 29 times 0) [i] based on linear OA(829, 30, F8, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,8)), using
(46, 75, 51258)-Net in Base 8 — Upper bound on s
There is no (46, 75, 51259)-net in base 8, because
- 1 times m-reduction [i] would yield (46, 74, 51259)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 6 741462 394323 631753 730645 708893 507582 988413 534705 291874 915310 188508 > 874 [i]