MinT - Best Known (10, 10+50, s)-Nets in Base 8

Best Known (10, 10+50, s)-Nets in Base 8

(10, 10+50, 46)-Net over F₈ — Constructive and digital

Digital (10, 60, 46)-net over F₈, using

net from sequence [i] based on digital (10, 45)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 9, N(F)Â =Â 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+50, 163)-Net in Base 8 — Upper bound on s

There is no (10, 60, 164)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁶⁰, 164, S₈, 50), but
- the linear programming bound shows that MÂ â‰¥ 295 614383 479442 048964 163625 500967 019202 231456 858009 381285 816613 407486 868627 350189 879345 466002 949051 613386 031720 039455 643001 150960 827446 364962 029568 / 183 566322 509149 519674 640201 988131 690574 707192 883120 970692 113601 083673 764214 942689 612725 325211 > 8⁶⁰ [i]