MinT - Best Known (150−55, 150, s)-Nets in Base 9

Best Known (150−55, 150, s)-Nets in Base 9

(150−55, 150, 740)-Net over F₉ — Constructive and digital

Digital (95, 150, 740)-net over F₉, using

t-expansion [i] based on digital (91, 150, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 75, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(150−55, 150, 1200)-Net over F₉ — Digital

Digital (95, 150, 1200)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−55, 150, 251937)-Net in Base 9 — Upper bound on s

There is no (95, 150, 251938)-net in base 9, because

1 times m-reduction [i] would yield (95, 149, 251938)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15210 316461 231291 058773 671980 861540 320902 931746 651068 089352 381877 739635 844483 963948 745948 491970 824474 676856 334317 267506 002301 870111 958120 191985 > 9¹⁴⁹ [i]