Best Known (10, 10+60, s)-Nets in Base 8
(10, 10+60, 46)-Net over F8 — Constructive and digital
Digital (10, 70, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
(10, 10+60, 120)-Net in Base 8 — Upper bound on s
There is no (10, 70, 121)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(870, 121, S8, 60), but
- the linear programming bound shows that M ≥ 4 235369 351545 742514 219122 566374 981712 662621 057642 042276 552070 238406 080823 368210 051322 299583 806396 796241 974406 581846 681802 501382 448896 540672 / 2539 335238 530089 078464 318738 877398 881731 476306 808873 698593 363590 524760 666963 > 870 [i]