Best Known (28−16, 28, s)-Nets in Base 64
(28−16, 28, 184)-Net over F64 — Constructive and digital
Digital (12, 28, 184)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- digital (3, 19, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- digital (1, 9, 80)-net over F64, using
(28−16, 28, 262)-Net in Base 64 — Constructive
(12, 28, 262)-net in base 64, using
- base change [i] based on digital (5, 21, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
(28−16, 28, 286)-Net over F64 — Digital
Digital (12, 28, 286)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6428, 286, F64, 16) (dual of [286, 258, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6428, 315, F64, 16) (dual of [315, 287, 17]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 315 | 642−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(6428, 315, F64, 16) (dual of [315, 287, 17]-code), using
(28−16, 28, 321)-Net in Base 64
(12, 28, 321)-net in base 64, using
- 12 times m-reduction [i] based on (12, 40, 321)-net in base 64, using
- base change [i] based on digital (2, 30, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 30, 321)-net over F256, using
(28−16, 28, 125304)-Net in Base 64 — Upper bound on s
There is no (12, 28, 125305)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 374 155077 153996 492978 592603 808097 335086 521703 548979 > 6428 [i]