MinT - Best Known (11, 11+67, s)-Nets in Base 8

Best Known (11, 11+67, s)-Nets in Base 8

(11, 11+67, 48)-Net over F₈ — Constructive and digital

Digital (11, 78, 48)-net over F₈, using

net from sequence [i] based on digital (11, 47)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
  - a function field by SÃ©mirat [i]

(11, 11+67, 116)-Net in Base 8 — Upper bound on s

There is no (11, 78, 117)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁷⁸, 117, S₈, 67), but
- the linear programming bound shows that MÂ â‰¥ 356 549751 883899 350685 835571 744207 842085 685740 745336 173842 355392 315151 882780 394149 917258 997648 990653 358959 354389 200896 / 12570 840222 192874 883804 439726 656819 075822 612445 > 8⁷⁸ [i]