Best Known (183, 183+35, s)-Nets in Base 3
(183, 183+35, 1480)-Net over F3 — Constructive and digital
Digital (183, 218, 1480)-net over F3, using
- t-expansion [i] based on digital (181, 218, 1480)-net over F3, using
- 2 times m-reduction [i] based on digital (181, 220, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 55, 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, 55, 370)-net over F81, using
- 2 times m-reduction [i] based on digital (181, 220, 1480)-net over F3, using
(183, 183+35, 9861)-Net over F3 — Digital
Digital (183, 218, 9861)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3218, 9861, F3, 2, 35) (dual of [(9861, 2), 19504, 36]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3218, 19722, F3, 35) (dual of [19722, 19504, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- linear OA(3208, 19683, F3, 35) (dual of [19683, 19475, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3172, 19683, F3, 29) (dual of [19683, 19511, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(310, 39, F3, 5) (dual of [39, 29, 6]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- OOA 2-folding [i] based on linear OA(3218, 19722, F3, 35) (dual of [19722, 19504, 36]-code), using
(183, 183+35, 4418003)-Net in Base 3 — Upper bound on s
There is no (183, 218, 4418004)-net in base 3, because
- 1 times m-reduction [i] would yield (183, 217, 4418004)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 34 301472 590282 302796 523772 651358 885898 461020 308901 860114 848433 897552 209952 832178 700720 794125 691763 307689 > 3217 [i]