Best Known (182, 220, s)-Nets in Base 3
(182, 220, 1480)-Net over F3 — Constructive and digital
Digital (182, 220, 1480)-net over F3, using
- t-expansion [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
(182, 220, 5670)-Net over F3 — Digital
Digital (182, 220, 5670)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3220, 5670, F3, 38) (dual of [5670, 5450, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(3220, 6581, F3, 38) (dual of [6581, 6361, 39]-code), using
- (u, u+v)-construction [i] based on
- linear OA(319, 20, F3, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,3)), using
- dual of repetition code with length 20 [i]
- linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using
- an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(319, 20, F3, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,3)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(3220, 6581, F3, 38) (dual of [6581, 6361, 39]-code), using
(182, 220, 1326604)-Net in Base 3 — Upper bound on s
There is no (182, 220, 1326605)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 926 150004 677983 075482 054426 920534 725735 670941 396774 969889 545477 585282 002425 358809 342752 846065 768534 931467 > 3220 [i]