Best Known (63, 63+33, s)-Nets in Base 8
(63, 63+33, 363)-Net over F8 — Constructive and digital
Digital (63, 96, 363)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 16, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (47, 80, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 40, 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, 40, 177)-net over F64, using
- digital (0, 16, 9)-net over F8, using
(63, 63+33, 520)-Net in Base 8 — Constructive
(63, 96, 520)-net in base 8, using
- base change [i] based on digital (39, 72, 520)-net over F16, using
- trace code for nets [i] based on digital (3, 36, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- trace code for nets [i] based on digital (3, 36, 260)-net over F256, using
(63, 63+33, 952)-Net over F8 — Digital
Digital (63, 96, 952)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(896, 952, F8, 33) (dual of [952, 856, 34]-code), using
- 855 step Varšamov–Edel lengthening with (ri) = (5, 3, 2, 1, 1, 1, 1, 0, 1, 1, 0, 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, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 33 times 0, 1, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 43 times 0, 1, 47 times 0, 1, 50 times 0, 1, 53 times 0, 1, 57 times 0) [i] based on linear OA(833, 34, F8, 33) (dual of [34, 1, 34]-code or 34-arc in PG(32,8)), using
- dual of repetition code with length 34 [i]
- 855 step Varšamov–Edel lengthening with (ri) = (5, 3, 2, 1, 1, 1, 1, 0, 1, 1, 0, 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, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 33 times 0, 1, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 43 times 0, 1, 47 times 0, 1, 50 times 0, 1, 53 times 0, 1, 57 times 0) [i] based on linear OA(833, 34, F8, 33) (dual of [34, 1, 34]-code or 34-arc in PG(32,8)), using
(63, 63+33, 223624)-Net in Base 8 — Upper bound on s
There is no (63, 96, 223625)-net in base 8, because
- 1 times m-reduction [i] would yield (63, 95, 223625)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 62 169699 019278 760997 495684 334495 532695 540670 204126 366589 791680 817595 637108 560594 845176 > 895 [i]