Best Known (72, 72+100, s)-Nets in Base 8
(72, 72+100, 100)-Net over F8 — Constructive and digital
Digital (72, 172, 100)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 58, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- digital (14, 114, 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 (8, 58, 35)-net over F8, using
(72, 72+100, 150)-Net over F8 — Digital
Digital (72, 172, 150)-net over F8, using
(72, 72+100, 161)-Net in Base 8
(72, 172, 161)-net in base 8, using
- base change [i] based on digital (29, 129, 161)-net over F16, using
- net from sequence [i] based on digital (29, 160)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 29 and N(F) ≥ 161, using
- net from sequence [i] based on digital (29, 160)-sequence over F16, using
(72, 72+100, 3526)-Net in Base 8 — Upper bound on s
There is no (72, 172, 3527)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 216534 864114 319352 234284 957669 159384 383472 885511 938256 732113 540957 994607 485843 311212 835232 441495 742744 608591 684559 818498 900433 705669 457768 483398 379168 051836 > 8172 [i]