Best Known (187, 233, s)-Nets in Base 3
(187, 233, 688)-Net over F3 — Constructive and digital
Digital (187, 233, 688)-net over F3, using
- 7 times m-reduction [i] based on digital (187, 240, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 60, 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, 60, 172)-net over F81, using
(187, 233, 2628)-Net over F3 — Digital
Digital (187, 233, 2628)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3233, 2628, F3, 46) (dual of [2628, 2395, 47]-code), using
- 419 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 8 times 0, 1, 10 times 0, 1, 14 times 0, 1, 18 times 0, 1, 23 times 0, 1, 28 times 0, 1, 35 times 0, 1, 41 times 0, 1, 46 times 0, 1, 51 times 0, 1, 55 times 0, 1, 59 times 0) [i] based on linear OA(3211, 2187, F3, 46) (dual of [2187, 1976, 47]-code), using
- an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- 419 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 8 times 0, 1, 10 times 0, 1, 14 times 0, 1, 18 times 0, 1, 23 times 0, 1, 28 times 0, 1, 35 times 0, 1, 41 times 0, 1, 46 times 0, 1, 51 times 0, 1, 55 times 0, 1, 59 times 0) [i] based on linear OA(3211, 2187, F3, 46) (dual of [2187, 1976, 47]-code), using
(187, 233, 321248)-Net in Base 3 — Upper bound on s
There is no (187, 233, 321249)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1476 576914 216468 127570 481506 748468 203194 712957 375765 242977 892595 902406 626981 290229 568225 443018 661060 663919 274955 > 3233 [i]