Best Known (125, 125+30, s)-Nets in Base 3
(125, 125+30, 688)-Net over F3 — Constructive and digital
Digital (125, 155, 688)-net over F3, using
- t-expansion [i] based on digital (124, 155, 688)-net over F3, using
- 1 times m-reduction [i] based on digital (124, 156, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 39, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 39, 172)-net over F81, using
- 1 times m-reduction [i] based on digital (124, 156, 688)-net over F3, using
(125, 125+30, 2300)-Net over F3 — Digital
Digital (125, 155, 2300)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3155, 2300, F3, 30) (dual of [2300, 2145, 31]-code), using
- 98 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 8 times 0, 1, 10 times 0, 1, 14 times 0, 1, 19 times 0, 1, 24 times 0) [i] based on linear OA(3140, 2187, F3, 30) (dual of [2187, 2047, 31]-code), using
- 1 times truncation [i] based on linear OA(3141, 2188, F3, 31) (dual of [2188, 2047, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3141, 2188, F3, 31) (dual of [2188, 2047, 32]-code), using
- 98 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 8 times 0, 1, 10 times 0, 1, 14 times 0, 1, 19 times 0, 1, 24 times 0) [i] based on linear OA(3140, 2187, F3, 30) (dual of [2187, 2047, 31]-code), using
(125, 125+30, 273505)-Net in Base 3 — Upper bound on s
There is no (125, 155, 273506)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 89 908042 348057 255140 645780 505040 419173 056716 159956 664183 140978 677856 571161 > 3155 [i]