Best Known (43, 43+36, s)-Nets in Base 64
(43, 43+36, 513)-Net over F64 — Constructive and digital
Digital (43, 79, 513)-net over F64, using
- t-expansion [i] based on digital (28, 79, 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
(43, 43+36, 546)-Net in Base 64 — Constructive
(43, 79, 546)-net in base 64, using
- (u, u+v)-construction [i] based on
- (8, 26, 258)-net in base 64, using
- 2 times m-reduction [i] based on (8, 28, 258)-net in base 64, using
- base change [i] based on digital (1, 21, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 21, 258)-net over F256, using
- 2 times m-reduction [i] based on (8, 28, 258)-net in base 64, using
- (17, 53, 288)-net in base 64, using
- 3 times m-reduction [i] based on (17, 56, 288)-net in base 64, using
- base change [i] based on digital (9, 48, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 48, 288)-net over F128, using
- 3 times m-reduction [i] based on (17, 56, 288)-net in base 64, using
- (8, 26, 258)-net in base 64, using
(43, 43+36, 2974)-Net over F64 — Digital
Digital (43, 79, 2974)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6479, 2974, F64, 36) (dual of [2974, 2895, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(6479, 4122, F64, 36) (dual of [4122, 4043, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(26) [i] based on
- linear OA(6471, 4096, F64, 36) (dual of [4096, 4025, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(6453, 4096, F64, 27) (dual of [4096, 4043, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(648, 26, F64, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,64)), using
- discarding factors / shortening the dual code based on linear OA(648, 64, F64, 8) (dual of [64, 56, 9]-code or 64-arc in PG(7,64)), using
- Reed–Solomon code RS(56,64) [i]
- discarding factors / shortening the dual code based on linear OA(648, 64, F64, 8) (dual of [64, 56, 9]-code or 64-arc in PG(7,64)), using
- construction X applied to Ce(35) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(6479, 4122, F64, 36) (dual of [4122, 4043, 37]-code), using
(43, 43+36, large)-Net in Base 64 — Upper bound on s
There is no (43, 79, large)-net in base 64, because
- 34 times m-reduction [i] would yield (43, 45, large)-net in base 64, but