MinT - Best Known (88−75, 88, s)-Nets in Base 8

Best Known (88−75, 88, s)-Nets in Base 8

(88−75, 88, 48)-Net over F₈ — Constructive and digital

Digital (13, 88, 48)-net over F₈, using

t-expansion [i] based on digital (11, 88, 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]

(88−75, 88, 56)-Net over F₈ — Digital

Digital (13, 88, 56)-net over F₈, using

net from sequence [i] based on digital (13, 55)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 13 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(88−75, 88, 140)-Net in Base 8 — Upper bound on s

There is no (13, 88, 141)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁸⁸, 141, S₈, 75), but
- the linear programming bound shows that MÂ â‰¥ 7404 537731 867996 917335 812746 502503 971527 459481 593565 381008 314347 711563 926825 036137 152674 630996 526390 391855 808891 938210 137154 260552 945788 098752 285695 124260 391640 629248 / 238 585864 169217 488077 461544 381172 839788 212158 730137 232623 561989 444129 805576 568494 650855 > 8⁸⁸ [i]