Best Known (229−46, 229, s)-Nets in Base 3
(229−46, 229, 688)-Net over F3 — Constructive and digital
Digital (183, 229, 688)-net over F3, using
- t-expansion [i] based on digital (181, 229, 688)-net over F3, using
- 3 times m-reduction [i] based on digital (181, 232, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 58, 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, 58, 172)-net over F81, using
- 3 times m-reduction [i] based on digital (181, 232, 688)-net over F3, using
(229−46, 229, 2409)-Net over F3 — Digital
Digital (183, 229, 2409)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3229, 2409, F3, 46) (dual of [2409, 2180, 47]-code), using
- 204 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) [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]
- 204 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) [i] based on linear OA(3211, 2187, F3, 46) (dual of [2187, 1976, 47]-code), using
(229−46, 229, 265373)-Net in Base 3 — Upper bound on s
There is no (183, 229, 265374)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 18 229923 186614 723835 571731 533636 177836 732767 006354 555650 256829 368455 337425 435300 112553 571115 419586 082428 903705 > 3229 [i]