Best Known (104−67, 104, s)-Nets in Base 8
(104−67, 104, 98)-Net over F8 — Constructive and digital
Digital (37, 104, 98)-net over F8, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
(104−67, 104, 121)-Net over F8 — Digital
Digital (37, 104, 121)-net over F8, using
- net from sequence [i] based on digital (37, 120)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 121, using
(104−67, 104, 1218)-Net in Base 8 — Upper bound on s
There is no (37, 104, 1219)-net in base 8, because
- 1 times m-reduction [i] would yield (37, 103, 1219)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1066 459470 376557 412647 492521 870135 381778 678641 583371 199029 955065 596570 540747 138024 186680 791020 > 8103 [i]