Best Known (99−30, 99, s)-Nets in Base 9
(99−30, 99, 740)-Net over F9 — Constructive and digital
Digital (69, 99, 740)-net over F9, using
- 7 times m-reduction [i] based on digital (69, 106, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 53, 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, 53, 370)-net over F81, using
(99−30, 99, 2655)-Net over F9 — Digital
Digital (69, 99, 2655)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(999, 2655, F9, 30) (dual of [2655, 2556, 31]-code), using
- 2555 step Varšamov–Edel lengthening with (ri) = (5, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 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, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 32 times 0, 1, 34 times 0, 1, 37 times 0, 1, 41 times 0, 1, 43 times 0, 1, 47 times 0, 1, 52 times 0, 1, 55 times 0, 1, 60 times 0, 1, 65 times 0, 1, 69 times 0, 1, 76 times 0, 1, 82 times 0, 1, 88 times 0, 1, 95 times 0, 1, 103 times 0, 1, 112 times 0, 1, 120 times 0, 1, 130 times 0, 1, 140 times 0, 1, 152 times 0, 1, 163 times 0, 1, 177 times 0, 1, 191 times 0) [i] based on linear OA(930, 31, F9, 30) (dual of [31, 1, 31]-code or 31-arc in PG(29,9)), using
- dual of repetition code with length 31 [i]
- 2555 step Varšamov–Edel lengthening with (ri) = (5, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 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, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 32 times 0, 1, 34 times 0, 1, 37 times 0, 1, 41 times 0, 1, 43 times 0, 1, 47 times 0, 1, 52 times 0, 1, 55 times 0, 1, 60 times 0, 1, 65 times 0, 1, 69 times 0, 1, 76 times 0, 1, 82 times 0, 1, 88 times 0, 1, 95 times 0, 1, 103 times 0, 1, 112 times 0, 1, 120 times 0, 1, 130 times 0, 1, 140 times 0, 1, 152 times 0, 1, 163 times 0, 1, 177 times 0, 1, 191 times 0) [i] based on linear OA(930, 31, F9, 30) (dual of [31, 1, 31]-code or 31-arc in PG(29,9)), using
(99−30, 99, 1594684)-Net in Base 9 — Upper bound on s
There is no (69, 99, 1594685)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 29512 777671 722734 685216 579629 360484 153105 113449 576660 969029 659018 939887 540990 237734 924363 885913 > 999 [i]