Best Known (197−36, 197, s)-Nets in Base 4
(197−36, 197, 1539)-Net over F4 — Constructive and digital
Digital (161, 197, 1539)-net over F4, using
- t-expansion [i] based on digital (160, 197, 1539)-net over F4, using
- 1 times m-reduction [i] based on digital (160, 198, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 66, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 66, 513)-net over F64, using
- 1 times m-reduction [i] based on digital (160, 198, 1539)-net over F4, using
(197−36, 197, 13310)-Net over F4 — Digital
Digital (161, 197, 13310)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4197, 13310, F4, 36) (dual of [13310, 13113, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(4197, 16419, F4, 36) (dual of [16419, 16222, 37]-code), using
- construction X applied to Ce(36) ⊂ Ce(30) [i] based on
- linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(36) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(4197, 16419, F4, 36) (dual of [16419, 16222, 37]-code), using
(197−36, 197, large)-Net in Base 4 — Upper bound on s
There is no (161, 197, large)-net in base 4, because
- 34 times m-reduction [i] would yield (161, 163, large)-net in base 4, but