MinT - Best Known (91, 91+51, s)-Nets in Base 9

Best Known (91, 91+51, s)-Nets in Base 9

(91, 91+51, 740)-Net over F₉ — Constructive and digital

Digital (91, 142, 740)-net over F₉, using

8 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]

(91, 91+51, 1274)-Net over F₉ — Digital

Digital (91, 142, 1274)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+51, 306508)-Net in Base 9 — Upper bound on s

There is no (91, 142, 306509)-net in base 9, because

1 times m-reduction [i] would yield (91, 141, 306509)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 353 362551 725649 874261 224450 598237 576382 258310 841929 324848 551036 625331 935332 793035 951660 776562 708178 406640 958686 766169 101261 817046 889769 > 9¹⁴¹ [i]