MinT - Best Known (88, 88+74, s)-Nets in Base 8

Best Known (88, 88+74, s)-Nets in Base 8

(88, 88+74, 354)-Net over F₈ — Constructive and digital

Digital (88, 162, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 81, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(88, 88+74, 380)-Net over F₈ — Digital

Digital (88, 162, 380)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+74, 18808)-Net in Base 8 — Upper bound on s

There is no (88, 162, 18809)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 200 122249 907004 801259 300486 273866 716243 516011 894416 550921 989970 250020 592205 071348 483326 962684 296447 576378 443693 653907 185315 021892 874754 903709 186344 > 8¹⁶² [i]