Best Known (149, 193, s)-Nets in Base 3
(149, 193, 600)-Net over F3 — Constructive and digital
Digital (149, 193, 600)-net over F3, using
- 31 times duplication [i] based on digital (148, 192, 600)-net over F3, using
- trace code for nets [i] based on digital (4, 48, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 48, 150)-net over F81, using
(149, 193, 1191)-Net over F3 — Digital
Digital (149, 193, 1191)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3193, 1191, F3, 44) (dual of [1191, 998, 45]-code), using
- 997 step Varšamov–Edel lengthening with (ri) = (15, 8, 4, 3, 3, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 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, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 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, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0) [i] based on linear OA(344, 45, F3, 44) (dual of [45, 1, 45]-code or 45-arc in PG(43,3)), using
- dual of repetition code with length 45 [i]
- 997 step Varšamov–Edel lengthening with (ri) = (15, 8, 4, 3, 3, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 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, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 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, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 14 times 0, 1, 14 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 17 times 0, 1, 17 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 20 times 0, 1, 20 times 0, 1, 21 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 25 times 0, 1, 26 times 0, 1, 27 times 0, 1, 28 times 0) [i] based on linear OA(344, 45, F3, 44) (dual of [45, 1, 45]-code or 45-arc in PG(43,3)), using
(149, 193, 69397)-Net in Base 3 — Upper bound on s
There is no (149, 193, 69398)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 121 474611 145051 922727 751881 334418 348642 456472 232097 512616 647545 451062 081576 139608 338645 541717 > 3193 [i]