Best Known (83, 111, s)-Nets in Base 3
(83, 111, 264)-Net over F3 — Constructive and digital
Digital (83, 111, 264)-net over F3, using
- trace code for nets [i] based on digital (9, 37, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
(83, 111, 528)-Net over F3 — Digital
Digital (83, 111, 528)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3111, 528, F3, 28) (dual of [528, 417, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3111, 728, F3, 28) (dual of [728, 617, 29]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(3111, 728, F3, 28) (dual of [728, 617, 29]-code), using
(83, 111, 18323)-Net in Base 3 — Upper bound on s
There is no (83, 111, 18324)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 91363 343129 807054 026477 187703 481802 724822 793838 414393 > 3111 [i]