Best Known (53, 53+65, s)-Nets in Base 8
(53, 53+65, 99)-Net over F8 — Constructive and digital
Digital (53, 118, 99)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 39, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (14, 79, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (7, 39, 34)-net over F8, using
(53, 53+65, 144)-Net over F8 — Digital
Digital (53, 118, 144)-net over F8, using
- t-expansion [i] based on digital (45, 118, 144)-net over F8, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 45 and N(F) ≥ 144, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
(53, 53+65, 3641)-Net in Base 8 — Upper bound on s
There is no (53, 118, 3642)-net in base 8, because
- 1 times m-reduction [i] would yield (53, 117, 3642)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 4592 991959 061111 713230 511717 635834 709612 279107 851600 997369 189766 570756 352331 736879 543561 309673 400370 695947 > 8117 [i]