Best Known (35, 35+32, s)-Nets in Base 64
(35, 35+32, 513)-Net over F64 — Constructive and digital
Digital (35, 67, 513)-net over F64, using
- t-expansion [i] based on digital (28, 67, 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
(35, 35+32, 516)-Net in Base 64 — Constructive
(35, 67, 516)-net in base 64, using
- 1 times m-reduction [i] based on (35, 68, 516)-net in base 64, using
- base change [i] based on digital (18, 51, 516)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 17, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (1, 34, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- digital (1, 17, 258)-net over F256, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (18, 51, 516)-net over F256, using
(35, 35+32, 2055)-Net over F64 — Digital
Digital (35, 67, 2055)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6467, 2055, F64, 2, 32) (dual of [(2055, 2), 4043, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6467, 4110, F64, 32) (dual of [4110, 4043, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(26) [i] based on
- linear OA(6463, 4096, F64, 32) (dual of [4096, 4033, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [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(644, 14, F64, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- construction X applied to Ce(31) ⊂ Ce(26) [i] based on
- OOA 2-folding [i] based on linear OA(6467, 4110, F64, 32) (dual of [4110, 4043, 33]-code), using
(35, 35+32, 3949807)-Net in Base 64 — Upper bound on s
There is no (35, 67, 3949808)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 10 329007 679114 590650 684276 019647 196667 791071 492700 692658 215702 086622 256488 321788 544538 314577 862898 958099 812112 073172 269590 > 6467 [i]