MinT - Best Known (155−107, 155, s)-Nets in Base 8

Best Known (155−107, 155, s)-Nets in Base 8

(155−107, 155, 98)-Net over F₈ — Constructive and digital

Digital (48, 155, 98)-net over F₈, using

t-expansion [i] based on digital (37, 155, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(155−107, 155, 144)-Net over F₈ — Digital

Digital (48, 155, 144)-net over F₈, using

t-expansion [i] based on digital (45, 155, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(155−107, 155, 1204)-Net in Base 8 — Upper bound on s

There is no (48, 155, 1205)-net in base 8, because

1 times m-reduction [i] would yield (48, 154, 1205)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 995357 740062 335433 353557 451721 613349 184577 757490 938131 647932 420326 004330 459060 130641 278536 994973 122140 679185 004989 143950 368246 487826 086472 > 8¹⁵⁴ [i]