Best Known (101, 101+49, s)-Nets in Base 9
(101, 101+49, 740)-Net over F9 — Constructive and digital
Digital (101, 150, 740)-net over F9, using
- t-expansion [i] based on digital (91, 150, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 75, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 75, 370)-net over F81, using
(101, 101+49, 2272)-Net over F9 — Digital
Digital (101, 150, 2272)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9150, 2272, F9, 49) (dual of [2272, 2122, 50]-code), using
- 2121 step Varšamov–Edel lengthening with (ri) = (7, 3, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 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, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 37 times 0, 1, 38 times 0, 1, 40 times 0, 1, 42 times 0, 1, 44 times 0, 1, 47 times 0, 1, 48 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 58 times 0, 1, 62 times 0, 1, 65 times 0, 1, 67 times 0, 1, 71 times 0, 1, 75 times 0, 1, 78 times 0, 1, 82 times 0, 1, 85 times 0, 1, 90 times 0, 1, 94 times 0, 1, 99 times 0) [i] based on linear OA(949, 50, F9, 49) (dual of [50, 1, 50]-code or 50-arc in PG(48,9)), using
- dual of repetition code with length 50 [i]
- 2121 step Varšamov–Edel lengthening with (ri) = (7, 3, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 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, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 22 times 0, 1, 23 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 30 times 0, 1, 31 times 0, 1, 33 times 0, 1, 35 times 0, 1, 37 times 0, 1, 38 times 0, 1, 40 times 0, 1, 42 times 0, 1, 44 times 0, 1, 47 times 0, 1, 48 times 0, 1, 51 times 0, 1, 54 times 0, 1, 56 times 0, 1, 58 times 0, 1, 62 times 0, 1, 65 times 0, 1, 67 times 0, 1, 71 times 0, 1, 75 times 0, 1, 78 times 0, 1, 82 times 0, 1, 85 times 0, 1, 90 times 0, 1, 94 times 0, 1, 99 times 0) [i] based on linear OA(949, 50, F9, 49) (dual of [50, 1, 50]-code or 50-arc in PG(48,9)), using
(101, 101+49, 1029253)-Net in Base 9 — Upper bound on s
There is no (101, 150, 1029254)-net in base 9, because
- 1 times m-reduction [i] would yield (101, 149, 1029254)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 15210 461048 236307 224318 288072 769562 305862 951035 997883 036208 750701 319237 362225 532250 461993 628637 221812 948468 727374 629512 592896 400239 883566 747009 > 9149 [i]