MinT - Best Known (149−51, 149, s)-Nets in Base 9

Best Known (149−51, 149, s)-Nets in Base 9

(149−51, 149, 740)-Net over F₉ — Constructive and digital

Digital (98, 149, 740)-net over F₉, using

t-expansion [i] based on digital (91, 149, 740)-net over F₉, using
- 1 times m-reduction [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]

(149−51, 149, 1724)-Net over F₉ — Digital

Digital (98, 149, 1724)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−51, 149, 567074)-Net in Base 9 — Upper bound on s

There is no (98, 149, 567075)-net in base 9, because

1 times m-reduction [i] would yield (98, 148, 567075)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1690 075527 814316 485518 012591 374225 531586 986649 985179 358738 610849 530869 970993 440168 920437 425608 502282 317969 051693 764893 610190 486704 763186 918745 > 9¹⁴⁸ [i]