Best Known (79, 114, s)-Nets in Base 9
(79, 114, 740)-Net over F9 — Constructive and digital
Digital (79, 114, 740)-net over F9, using
- 12 times m-reduction [i] based on digital (79, 126, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 63, 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, 63, 370)-net over F81, using
(79, 114, 2696)-Net over F9 — Digital
Digital (79, 114, 2696)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9114, 2696, F9, 35) (dual of [2696, 2582, 36]-code), using
- 2581 step Varšamov–Edel lengthening with (ri) = (5, 3, 1, 1, 1, 1, 1, 1, 1, 0, 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, 4 times 0, 1, 0, 0, 0, 1, 5 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, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 34 times 0, 1, 36 times 0, 1, 38 times 0, 1, 41 times 0, 1, 44 times 0, 1, 48 times 0, 1, 50 times 0, 1, 54 times 0, 1, 57 times 0, 1, 62 times 0, 1, 66 times 0, 1, 70 times 0, 1, 75 times 0, 1, 81 times 0, 1, 86 times 0, 1, 91 times 0, 1, 98 times 0, 1, 105 times 0, 1, 112 times 0, 1, 119 times 0, 1, 127 times 0, 1, 136 times 0, 1, 146 times 0, 1, 155 times 0, 1, 166 times 0) [i] based on linear OA(935, 36, F9, 35) (dual of [36, 1, 36]-code or 36-arc in PG(34,9)), using
- dual of repetition code with length 36 [i]
- 2581 step Varšamov–Edel lengthening with (ri) = (5, 3, 1, 1, 1, 1, 1, 1, 1, 0, 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, 4 times 0, 1, 0, 0, 0, 1, 5 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, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 31 times 0, 1, 34 times 0, 1, 36 times 0, 1, 38 times 0, 1, 41 times 0, 1, 44 times 0, 1, 48 times 0, 1, 50 times 0, 1, 54 times 0, 1, 57 times 0, 1, 62 times 0, 1, 66 times 0, 1, 70 times 0, 1, 75 times 0, 1, 81 times 0, 1, 86 times 0, 1, 91 times 0, 1, 98 times 0, 1, 105 times 0, 1, 112 times 0, 1, 119 times 0, 1, 127 times 0, 1, 136 times 0, 1, 146 times 0, 1, 155 times 0, 1, 166 times 0) [i] based on linear OA(935, 36, F9, 35) (dual of [36, 1, 36]-code or 36-arc in PG(34,9)), using
(79, 114, 1975873)-Net in Base 9 — Upper bound on s
There is no (79, 114, 1975874)-net in base 9, because
- 1 times m-reduction [i] would yield (79, 113, 1975874)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 675159 350823 117296 715054 836527 097314 904870 105665 414686 040326 919580 803048 617176 414982 469988 971365 989473 646865 > 9113 [i]