Best Known (99−33, 99, s)-Nets in Base 7
(99−33, 99, 200)-Net over F7 — Constructive and digital
Digital (66, 99, 200)-net over F7, using
- 71 times duplication [i] based on digital (65, 98, 200)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (16, 32, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 16, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- trace code for nets [i] based on digital (0, 16, 50)-net over F49, using
- digital (33, 66, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 33, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- trace code for nets [i] based on digital (0, 33, 50)-net over F49, using
- digital (16, 32, 100)-net over F7, using
- (u, u+v)-construction [i] based on
(99−33, 99, 894)-Net over F7 — Digital
Digital (66, 99, 894)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(799, 894, F7, 33) (dual of [894, 795, 34]-code), using
- 794 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 1, 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, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 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, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 34 times 0, 1, 36 times 0, 1, 39 times 0, 1, 41 times 0, 1, 44 times 0, 1, 47 times 0, 1, 50 times 0) [i] based on linear OA(733, 34, F7, 33) (dual of [34, 1, 34]-code or 34-arc in PG(32,7)), using
- dual of repetition code with length 34 [i]
- 794 step Varšamov–Edel lengthening with (ri) = (6, 3, 2, 1, 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, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 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, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 28 times 0, 1, 30 times 0, 1, 31 times 0, 1, 34 times 0, 1, 36 times 0, 1, 39 times 0, 1, 41 times 0, 1, 44 times 0, 1, 47 times 0, 1, 50 times 0) [i] based on linear OA(733, 34, F7, 33) (dual of [34, 1, 34]-code or 34-arc in PG(32,7)), using
(99−33, 99, 170054)-Net in Base 7 — Upper bound on s
There is no (66, 99, 170055)-net in base 7, because
- 1 times m-reduction [i] would yield (66, 98, 170055)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 66015 559540 906824 076919 349869 465265 129855 592908 838068 296041 751471 420697 437372 744353 > 798 [i]